Answer:3/10
Step-by-step explanation:
f (t) = Atne(−bt)
The values A, n, and b are the parameters of the function.
This function accurately represents the way a drug interacts in the bloodstream. Studying
this function is essential to doctors and pharmacists because it allows them to administer
dosages of medicine correctly.1
A drug dose is being designed for a 90kg male patient. The amount of the drug in the
patient’s bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is given
by a surge function.
Any positive value of A can be achieved by increasing or decreasing the amount of
medicine given. However, depending on the type of delayed release mechanism selected
there are choices possible for the value of the pair (n,b): The achievable pairs are listed in
the table below.
Delay Type n value b value
Extended 2 0.3
Medium 3 0.5
Rapid 3 0.7
The medical requirements for the treatment are:
• The dose (in ng/ml) may not exceed 100 at any time.
• The dose must fall to be at or below 20 ng/ml by 24 hours.
Within these parameters, the treatment effect will be measured in ng/ml-hours. (1
ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtain
the maximum possible treatment effect while ensuring the requirements are met.. For each Delay Type, determine the value of A (dosage amount) that maximizes treat-
ment effect for that Delay Type while meeting medical requirements.
2. Determine which Delay Type (assuming optimal dosage) will maximize treatment ef-
fect.
3. For the Delay Type and dosage level you selected above,
(a) determine the treatment effect over the first 24 hours.
(b) determine the residual treatment effect for time after the first 24 hours
We can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml
How to solveTo determine the optimal dosage amount A for each Delay Type, we need to first define the surge function for each delay type as:
Extended: f(t) = [tex]At^2e^-^0^.^3^t[/tex]
Medium: f(t) = [tex]At^3e^-^0^.^5^t[/tex]
Rapid: f(t) = [tex]At^3e^-^0^.^7^t[/tex]
To find the optimal dosage amount A, we need to maximize the treatment effect while ensuring that the dose does not exceed 100ng/ml at any time and falls to be at or below 20ng/ml by 24 hours.
The treatment effect can be calculated by integrating the surge function over time from 0 to 24 hours and then adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20ng/ml
For the Delay Type and dosage level selected, we can calculate the treatment effect over the first 24 hours by integrating the surge function from 0 to 24 hours.
Then, we can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml..
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Compare and contrast the direct write-off method and the allowance method for bad debts.
At a minimum, please consider the following in your answer:
When is the expense for uncollected accounts receivable recognized under each method?
Why is the direct write-off method not considered to follow generally accepted accounting
The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.
How do we explain?When an account is found to be uncollectible, the direct write-off method records the expense for uncollected accounts receivable. This approach involves simply writing off the uncollectible account as a bad debt expense and deducting the outstanding quantity from the accounts receivable total.
Despite being quite easy to understand and basic, this method does not adhere to generally accepted accounting principles (GAAP) because it does not match expenses to the time period during which income was generated.
In contrast, the allowance approach establishes an allowance for doubtful accounts contra-asset account and estimates the amount of uncollectible accounts before recognizing the expense for uncollected accounts receivable.
This allowance account is used to lower the balance of accounts receivable to the anticipated amount of collection. Instead of when the account is found to be uncollectible, the expense is recognized at the time the estimate is made. Because it matches the expense to the time period in which the revenue was received, this method is thought to be more accurate than the direct write-off method.
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The top prism is 10 x 5 x 5 this one has me all kinds of confused
The volume of the complete prism is 1625 cubic in
How to find the volume of the figureThe volume of the figure is solved by dividing the figure into two sections and solving for each volume then adding the individual volume together.
The divisions are section 1 and section 2
section 1 has dimensions: 20 x 15 x 5
volume = 20 x 15 x 5 = 1500 cubic in
section 2 has dimensions: 5 x 5 x 5
volume = 5 x 5 x 5 = 125 cubic in
Volume of the complete figure
section 1 + section 2
= 1500 cubic in + 125 cubic in
= 1625 cubic in
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PLEASE HELP ME
Sophie deposited money into an account in which interest is compounded
semiannually at a rate of 2.2%. She made no other deposits or withdrawals and the
total amount in her account after 13 years was $22,099.87. How much did she
deposit? Round answer to nearest whole number. Do not include units in the
answer. Be sure to attach your work for credit.
By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.
What is compound interest?Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).
According to given information:We can use the formula for compound interest to solve this problem. The formula is:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = the total amount in the account
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know the values for A, r, n, and t, so we can solve for P:
[tex]A = P(1 + r/n)^{(nt)[/tex]
[tex]22,099.87 = P(1 + 0.022/2)^{(2*13)[/tex]
[tex]22,099.87 = P(1.011)^{26[/tex]
22,099.87 = 1.329P
P = 22,099.87 / 1.329
P = 16,637.55
Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.
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A number k multiplied by 4 is less than -3/2
Answer:
[tex]4k < -\frac{3}{2}[/tex]
Step-by-step explanation:
"A number k multiplied by 4 is less than -3/2"
First, let's look at the first part:
"A number k..."
We know the number we are operating is called k.
Let's look at the second part.
"...multiplied by 4..."
Now, we are multiply k by 4. After doing so, we get:
[tex]4k[/tex]
Finally, let's look at the last part.
"...is less than -3/2"
The quantity "a number k multiplied by 4" (or 4k) is less than -3/2.
We can rewrite this as:
[tex]4k < -\frac{3}{2}[/tex]
An individual depositing in a non-IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account.
Sarah, who is five years from retirement, receives a $10,000 bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 8 percent nominal interest, and Sarah is in the 30 percent tax bracket in every year (including her retirement year)
If Sarah invests in the normal savings account, her net value (after taxes) five years from now will be?:
The net value of the $10,000 bonus in a normal savings account after taxes and interest in five years will be $9,181.
What is the net value of Sarah's $10,000 bonus in a normal savings account after taxes and interest in five years?Assuming an 8 percent nominal interest rate and a 30 percent tax bracket, the after-tax return on the normal savings account is 5.6 percent. Thus, after five years, the $10,000 bonus will grow to $14,693.
However, since Sarah is in the 30 percent tax bracket in every year, she will owe taxes on the interest income earned each year. This reduces the after-tax return to 3.92 percent. Therefore, in five years, the $10,000 bonus in the normal savings account will be worth $9,181 after taxes.
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DETERMINE IF THE SEQUENCES ARE ARITHMETIC, IF SOFIND THE COMMONDIFFERENCE, THE 52 TERM, AND EXPLICIT FORMULA
31, -69, -169, -269
The common difference of the sequence is - 100.
The explicit formula of the sequence is 131 - 100n.
The 52 term of the sequence is -5069.
How to find the explicit formula of a sequence?Let's find the explicit formula of the arithmetic sequence as follows:
31, -69, -169, -269
We will find the common difference and the 52 terms.
Therefore,
a + (n + 1)d = nth term
where
a = first termd = common differencen = number of termsTherefore,
d = common difference = -69 - 31 = - 100
Therefore,
nth term = 31 + (n - 1)-100
nth term = 31 - 100n + 100
nth term = 131 - 100n
Let's find the 52 term
Hence,
52 term = 131 - 100(52)
52 term = 131 - 5200
52 term = -5069
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Here are the endpoints of the segments below...(full question in picture) *20 POINTS*
1) The length of the segments BC =√53 FG =√53 JK =√53
2) The statements that are true are;
BC ≅ FG
BC ≅ JK
FG ≅ JK
How do we find the lengths of the segments?
To find the lengths of the segments, we use the formula d = √((x2 - x1)² + (y2 - y1)²)
For BC, it would be √((1 - (-6))² + (2 - 4)²) = √53.
It would ordinarily be 7.3. However, since approximations are not needed, it has been left in the form of squareroot
For FG: √((-5 - (-7))² + (-1 - 6)²) = √53.
The answers provided are based on the questions seen in the image
Here are the endpoints of the segment BC, FG and JK.
B (-6, 4) C (1, 2) F (-7, 6), G (-5, -1) J (1, -8), K (3, -1)
Find the length of each segment. give an exact answer (not a decimal approximate)
BC = FG = JK =
Check all the statement that are true below;
BC ≅ FG
BC ≅ JK
FG ≅ JK
None of these are true.
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50 points. use rotation tool in top right to flip upright.
Answer:
(a) 56%
(b) 28%
Step-by-step explanation:
Hope this helps! :)
Pete is twice as old as chris. Seven years ago the sum of their ages was 31. Find their ages now
Answer:
Step-by-step explanation:
Answer: Pete is twice as old as Chris.p = 2c Seven years ago the sum of their ages were 31.(p-7) + (c-7) = 31p + c - 14 = 31p + c = 31 + 14p + c = 45Find their ages now replace p with 2c2c + c = 453c = 45c = 45/3c = 15 is Chris's agethenp = 2(15)p = 30 is Pete's age::Check solutions in the statement"Seven years ago the sum of their ages were 31"30-7 + 15-7 = 31
Determine how many liters a right circular cylindrical tank holds if it is 5 m long and 13 m in diameter.
The tank holds about _____ liters of liquid.
(Round to the nearest thousand as needed.)
The right circular cylindrical tank which is 5 m long and 13 m in diameter holds about 663,325 liters of liquid approximately.
The formula to find the volume of a right cylindrical tank is
V = πr²h, where 'r' is the radius and 'h' is the height.
Given that, the height is 5 m and the diameter is 13 m.
Radius = Diameter/2.
Radius = 13/2 = 6.5 m.
We know that, π = 3.14.
Now, we can substitute the values in the formula.
V = 3.14×(6.5)²×5.
V = 3.14×6.5×6.5×5
V = 663.325 cubic meters.
Now, we have to convert cubic meters into liters.
We need to multiply by 1000 as a thousand liters are in one cubic meter.
663.325×1000 = 663,325.
Therefore, the tank holds about 663,325 liters of liquid approximately.
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rationalize the denominator [tex]\frac{6}{\sqrt{x} 2\\}[/tex]
The rationalized form of the expression 6/√x is 6√x/x.
Rationalizing the denominatorFrom the question, we have the following parameters that can be used in our computation:
6/√x
To rationalize the denominator of 6/√x, we can multiply both the numerator and denominator by √x.
This gives:
6/√x * √x/√x = 6√x/x
So the rationalized form of 6/√x is 6√x/x.
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BRAINLIEST FOR RIGHT ANSWER
A cylinder has a volume of 517 cm³. What is the volume of a cone that has the same
size base and height as the cylinder. Write your answer in terms of pie
the volume of cone is [blank] pie cm^3
Answer:
[tex]\pi {r}^{2}h = 51\pi[/tex]
[tex] \frac{1}{3} \pi {r}^{2} h = \frac{1}{3} \times 51\pi= 17\pi[/tex]
The volume of the cone is 17π cubic centimeters.
need answers 5. , 6. , 7. , whoever gives all ill give brainliest!! please im gonna fail this class and im about to graduateee
Answer:
5)
$332.19
6)
$16,857.36
7)
$248.91
Step-by-step explanation:
monthly premium = Base Rate * [tex]\frac{Monthly Payroll}{100}[/tex]
5)
given:
Base rate = $2.24
Monthly payroll = $14,830.00
unknown = monthly premium
[tex]2.24 * \frac{14,830.00}{100}[/tex] = $332.192≈$332.19
6)
given:
Base rate = $19.89
Monthly payroll = $84,752.96
unknown = monthly premium
[tex]19.89 * \frac{84,752.96}{100}[/tex] = $16,857.364≈$16,857.36
7)
given:
Base rate = $2.90
Monthly payroll = $8,582.94
unknown = monthly premium
[tex]2.90 * \frac{8,582.94}{100}[/tex]=$248.90526≈$248.91
HELP QUICKLY PLEASE!!!
What are the x-intercepts of the quadratic function shown?
Answer:
D. 1,0 & -3,0
Step-by-step explanation:
because the two lines pass through points 1,0 and -3,0 at the x-axis
Answer:
your answer is D. 1,0 & -3,0
Step-by-step explanation:
Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. Select the appropriate response. With separate lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of 29 customers the waiting times have a standard deviation of 4.9 minutes. Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with separate lines. Select the correct test statistic and critical value.
Test statistic: x^2 = 18.462. Critical value: x^2 = 15.308
Test statistic: x^2 = 20.692. Critical value: x^2 = 15.308
Test statistic: x^2 = 20.692. Critical value: x^2 = 7.815, 15.308
Test statistic: x^2 = 18.462. Critical value: x^2 = 7.815, 15.308
Find the geometric mean of 5 and 320.
A. 35
B. 40
C. 45
D. 50
Answer: 40
Step-by-step explanation:
math
What is the best type of graph for the data set below?
The best type of graph for the data set below is a bar graph. So the correct option is A.
Describe bar graphThe pictorial representation of data which is generally grouped, in the form of vertical or horizontal rectangle-shaped bars is called a bar graph. In this type of graph, the length of bars is a representation of the measure of data. They are also called bar charts. In statistics, bar graphs are one of the ways of data handling.
Statistics is the collection, presentation, analysis, organization, and interpretation of data observations. There are various methods for the representation of this statistical data. These can be tables, bar graphs, pie charts, histograms, frequency polygons, etc.
There are three main characteristics of bar graphs. These are:
It helps in comparing the different sets of data among different groups.
The relationship using two axes is shown where the categories are on one axis and the values are on the other axis.
Major changes in data over time are shown.
Therefore the correct option is A.
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The complete question is:
which of the following satisfies ? 3m-5=10
Answer:3-7=5
Step-by-step explanation: 3-7=5
HELP ASAP ASAP PLS PLS ALSO BRAINLIEST
A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
4 8 one half
6
At this rate, how much sauce and oregano will be needed to make 6 servings?
The recipe will need 12 cups of sauce and three fourths teaspoons of oregano for 8 servings.
The recipe will need 12 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and three fourths teaspoons of oregano for 8 servings
The amounts needed to make 6 servings are given as follows:
Sauce: 12 servings.Oregano: 3/4 teaspoons.How to obtain the amounts?The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.
From the first line of the table, we get the amounts of sauce and oregano per serving are follows:
Sauce: 8/4 = 2 cups.Oregano: 0.5/4 = 1/8 teaspoons per serving.Hence the amounts for six servings are given as follows:
Sauce: 6 x 2 = 12 servings.Oregano: 6 x 1/8 = 6/8 = 3/4 teaspoons.More can be learned about proportions at https://brainly.com/question/24372153
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Making observations often involves:
A. forming a hypothesis, finding answers, and planning experiments.
OB. forming a hypothesis, asking questions, and writing articles.
C. asking questions, identifying problems, and gaining new
information.
D. finding ansers, making predictions, and identifying problems.
The correct statement is C. asking questions, identifying problems, and gaining new information is the most accurate option.
What is observation?The definition of "observation" given by Merriam-Webster is "an act of recognizing and noting a fact or occurrence often involving measurement with instruments," or "a record or description so obtained."
C. asking questions, identifying problems, and gaining new information is the most accurate option.
Making observations often involves the process of asking questions, identifying problems, and gaining new information. Observations are made to gather data and information about a phenomenon or event, which can then be used to answer questions or develop hypotheses for further research.
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find a. round to the nearest tenth. a=? cm
The value of (a) in given triangle is approximately 7.44 cm.
What do you mean by triangle?A triangle is a three-sided polygon consisting of three sides and three vertices. The most important property of a triangle is that the sum of its interior angles is 180 degrees.
Let ΔABC is a triangle
Given ∠ B = 75°
∠ C = 31.8°
AB = 12cm
AC = 22cm
find BC = ?
We can use the law of cosines to solve for BC:
BC² = AB² + AC² – 2(AB)(AC)cos(B)
We know that angle B = 75 degrees, so we can substitute:
BC² = 12² + 22² - 2(12)(22)cos(75)
Evaluating cos(75) with a calculator, we get:
BC² ≈ 144 + 484 - 572.59
BC² ≈ 55.41
Taking the square root of both sides gives us:
BC ≈ 7.44
Therefore, BC is approximately 7.44 cm.
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Recite the numbers in
each row.
29
42
77
30
43
78
31 32 33
44
45 46
79
80
81
го
Copyright © A Dab of Glue W
Note to recite the numbers, you have repeat alound the tiven numbers. Often, the purpose of recitation is to memorize and become aquatinted with.
Why do a recitation ?Recitation is often a smaller subset of a larger lecture course, commonly conducted by teaching assistants, meant to offer time for conceptual knowledge application and extension of training that happens in lecture through problem-solving or discussion.
Consider this a learning process in which knowledge is recalled from memory.
You have been handed numbers to recite in this case. Reciting numbers can help you increase your numeric intelligence.
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Brainliest and extra points for right answer.
Use the graph to answer the question.
Graph of polygon ABCDE with vertices at negative 1 comma negative 4, negative 1 comma negative 1, 3 comma negative 1, 3 comma negative 4, 1 comma negative 6. A second polygon A prime B prime C prime D prime E prime with vertices at 13 comma negative 4, 13 comma negative 1, 9 comma negative 1, 9 comma negative 4, 11 comma negative 6.
Determine the line of reflection.
Reflection across the x-axis
Reflection across x = 6
Reflection across y = −3
Reflection across the y-axis
Answer:
The question is asking about the line of reflection that would transform polygon ABCDE to its image A' B' C' D' E'.
To determine the line of reflection, we need to identify the axis or line that reflects each point of polygon ABCDE to its corresponding point on polygon A' B' C' D' E'.
Looking at the coordinates of the vertices, we can see that the x-coordinates of the corresponding points are the same, but the y-coordinates are opposite in sign. This suggests that the line of reflection is parallel to the x-axis.
Furthermore, we can see that the reflected image is below the original polygon, so the line of reflection must be the x-axis itself, reflecting the polygon downward.
Therefore, the correct answer is "Reflection across the x-axis."
5You can form a right triangle by cutting a _______ in half diagonally.
You can form a right triangle by cutting a square in half diagonally.
A square is a quadrilateral with four equal sides and four right angles. When a square is cut in half diagonally, it forms two congruent right triangles. The two halves of the square, which are the two legs of the right triangle, are equal in length.
The diagonal of the square, which is the hypotenuse of the right triangle, can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
Therefore, in a right triangle formed by cutting a square in half diagonally, the length of the hypotenuse can be found by taking the square root of the sum of the squares of the lengths of the two legs.
In summary, cutting a square in half diagonally allows us to form two congruent right triangles with equal leg lengths, making it a suitable shape to form a right triangle.
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17 feet 2 inches= Inches
Answer:
206 inches
Step-by-step explanation:
1 feet = 12 inches
17 feet = 17 x 12 = 204 inches
17 feet 2 inches = 204 + 2 = 206 inches
So, 17 feet 2 inches = 206 inches
NO LINKS!! URGENT HELP PLEASE!!!
Select all that apply
c. Symmetric with respect to the origin
Answer:
To determine if the given equations are symmetric with respect to the origin, we need to check if replacing x with -x and y with -y results in the same equation.
For the equations given:
y=7x-4 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=-7x+4, which is not the same equation.
y= -x+7 is not symmetric with respect to the origin since replacing x with -x and y with -y gives y=x-7, which is not the same equation.
y = -7x^2 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y = -7(-x)^2, which simplifies to -y = -7x^2. Thus, the equation remains the same.
y = 6x^2 - 9 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y = 6(-x)^2 - 9, which simplifies to -y = 6x^2 - 9. Thus, the equation is not the same.
x=1/4 y^2 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -x = 1/4 (-y)^2, which simplifies to -x = 1/4 y^2. Thus, the equation is not the same.
x = -y^2 + 9 is symmetric with respect to the origin since replacing x with -x and y with -y gives -x = -(-y)^2 + 9, which simplifies to -x = -y^2 + 9. Thus, the equation remains the same.
y=-1/6 x^3 is symmetric with respect to the origin since replacing x with -x and y with -y gives -y=-1/6(-x)^3, which simplifies to -y=-1/6 x^3. Thus, the equation remains the same.
y=x^3-1 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=(-x)^3-1, which simplifies to -y=-x^3-1. Thus, the equation is not the same.
y=sqrt(x) is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x), which is not the same equation.
y=sqrt(x)-6 is not symmetric with respect to the origin since replacing x with -x and y with -y gives -y=sqrt(-x)-6, which is not the same equation.
Therefore, the only equation that is symmetric with respect to the origin is y = -7x^2.
Answer:
i can only see b not c
Step-by-step explanation:
Type the correct answer in each box. If necessary, use / for the fraction bar. If 3 + 2i / 2 - 3i
The correct term in each box, if necessary, use / for the fraction bar are a = 1/7-4i, b = 1/13.
What is a fraction bar?In mathematics, a fraction bar is a visual representation of fractions that facilitates fraction comparison and fraction operation. Part-to-whole representational models like fraction bars or fraction strips are used. One unit out of a whole is represented by each segment of a fraction bar.
We need to be aware of an aspect of imaginary numbers in order to determine the values of variables a and b. The following rule applies to the hypothetical unit:
Therefore, the correct terms are 1/7-4i, b = 1/13.
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What is the measure of angle x?
Enter your answer in the box.
Answer:
43
Step-by-step explanation:
at the upper horizontal plane the angles add up to 180 degrees so you add the right angle with the 47 degrees and then you subtract the answer from180 degrees.the value you obtain is oppositely equal to the value of x hence,43
Write the equation of an exponential function that passes through the points
(1,12) and (3,108)
Answer:
[tex]f(x)=4(3)^x[/tex]
Step-by-step explanation:
The general equation for an exponential function is:
[tex]\boxed{f(x) = ab^x}[/tex]
where:
a is the initial value or y-intercept.b is the base or growth factor.To find the values of a and b that satisfy the given conditions, we can use the two points (1, 12) and (3, 108) to form a system of equations:
[tex]\begin{cases}12 = ab^1\\108 = ab^3\end{cases}[/tex]
Divide the second equation by the first equation to eliminate a:
[tex]\dfrac{ab^3}{ab} = \dfrac{108}{12}[/tex]
[tex]b^2=9[/tex]
[tex]\sqrt{b^2}=\sqrt{9}[/tex]
[tex]b=3[/tex]
Substitute the found value of b into the first equation and solve for a:
[tex]12&=3a[/tex]
[tex]\dfrac{12}{3}=\dfrac{3a}{3}[/tex]
[tex]4=a[/tex]
[tex]a=4[/tex]
Therefore, the equation of the exponential function that passes through the points (1, 12) and (3, 108) is:
[tex]\boxed{f(x) = 4(3)^x}[/tex]
Answer:
y=4(3^x).Step-by-step explanation:
To find the equation of an exponential function passing through the given points (1,12) and (3,108),
we can use the standard exponential form y=a(b^x). We know that when x=1, y=12,
so we can substitute these values into the equation to find a.
So 12 = a(b^1). Similarly, when x=3, y=108, so 108 = a(b^3). We can divide the second equation by the first to eliminate a and get (108/12) = b^2, or 9 = b^2. Thus, b=3 (taking only the positive root). We can now substitute this value of b into either equation to find a. Using the first equation, we get 12 = a(3^1), so a=4. Therefore, the exponential function passing through the given points is y=4(3^x).