The population of a colony of bacteria can be modeled by the function P(t) = 19,300(5)^t, where t is the elapsed time
in hours. What is the inverse function?
Answers
Answer:
C. P–1(t) = log5 (StartFraction t Over 19,300 EndFraction)
Step-by-step explanation:
The inverse function of P(t) is [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex]
What is an inverse function?The inverse function is a function obtained by reversing the given function. An inverse is a function that serves to “undo” another function. The domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.
For the given situation,
The function P(t) = 19,300(5)^t, where t is the elapsed time in hours.
Steps to find inverse function:
Step 1: Replace P(t) as y
[tex]P(t) = 19,300(5)^t[/tex]
⇒ [tex]y= 19,300(5)^{t}[/tex]
Step 2: interchange t and y
⇒ [tex]t = 19,300(5)^y[/tex]
Step 3: Now solve for y
⇒ [tex]\frac{t}{19300} =5^y[/tex]
By law of logarithm,
[tex]a^{x} = y[/tex]
⇒ [tex]log_{a} y=x[/tex]
Thus the equation becomes,
⇒ [tex]log_{5} \frac{t}{19300}=y[/tex]
Step 4: Now replace y as [tex]P^{-1}( t)[/tex]
⇒ [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex]
Hence we can conclude that the inverse function of P(t) is [tex]P^{-1} (t)=log_{5}( \frac{t}{19300})[/tex].
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Related Questions
Evaluate and simplify the following complex fraction.
Answers
Answer:
The answer is
[tex] - \frac{10}{7} \: \: \: or \: \: - 1 \frac{3}{7} [/tex]Step-by-step explanation:
[tex] \frac{ - \frac{5}{7} }{ \frac{2}{4} } [/tex]First of all we can write the fraction as
[tex] - \frac{5}{7} \div \frac{2}{4} [/tex]Simplify the second fraction
That's
[tex] \frac{2}{4} = \frac{1}{2} [/tex]So we have
[tex] - \frac{5}{7} \div \frac{1}{2} [/tex]Next change the division sign to multiplication sign and reverse the second fraction
That's
[tex] -\frac{5}{7} \times \frac{2}{1} [/tex]Multiply the terms
We have the final answer as
[tex] - \frac{10}{7} \: \: \: or \: \: - 1 \frac{3}{7} [/tex]Hope this helps you
Please help me figure this out
Answers
Answer:3⁴ and 81¹
Step-by-step explanation:
3⁹= 19683
3⁴= 81
-9²= -81
9⁹= 387,420,489
81¹= 81
Select the correct answer for each statement. (k+2, k+3 , k+4) or (k+10, k+12, k+14) will yield consecutive odd integers. (k+6, k+8 , k+10) or (k+1, k+2, k+3) will yield consecutive integers.
Answers
Answer:
Step-by-step explanation:
one
The only really certain way of getting an odd integer is to do 2k + 1. Therefore the answer should be something like 2k+1, 2k+3, 2k + 5
The best I can do for the first one is to assume that k is odd and that the answer is k + 10, k+12, k+14, but I would ask your instructor if this is merely the best answer out of a poor lot or if the question really has no answer.
Two things should be noted.
1. k has to be odd.
2. The first choice has to give consecutive integers because what is added on is 2 3 and 4. Those numbers are consecutive.
Two
k+1, k+2, k+3. See point 2 above. k is a constant and any number. 1,2,3 are consecutive so the results are consecutive. Even if k < 0 the numbers will be consecutive.
k= - 10
k+1 = - 9
k+2 = -8
k+3 = - 7
These are consecutive.
Your first choice will give either consecutive odd or even numbers depending on what k is.
If k = even, then k+6, k+ 8, k+10 will all be even.
If k = odd then the givens will be odd.
2k+9, 2k+11, 2k+13 will yield consecutive odd integers.
k+6, k+8, k+10 will yield consecutive integers.
whats x/7 = 4 in one step equations
Answers
Answer: x = 28
Step-by-step explanation: You multiply each place by 7 to get the x by itself and you get 28 as an answer
Answer:
28
Step-by-step explanation:
x/7=4
x=4*7
x=28
Which is a pair of vertical angles? ∠VRU and ∠SRT ∠TRS and ∠VRW ∠TRV and ∠WRU ∠WRV and ∠SRW
Answers
Answer:
b
Step-by-step explanation:
jus did it
Mrs. Yakubov needs to distribute 4 colored pencils and 3 glue sticks to the 6 tables in her classroom. Which expression represents the number of materials being distributed this situation? 6(4 + 3) 4(3 + 6) 3(4 + 6)
Answers
Answer:
[tex]6(4 + 3)[/tex]
Step-by-step explanation:
Given
Pencils = 4
Glue = 3
Required
Distribute these to 6 tables
Represent the pencils with P and Glue with G
The distribution to 6 tables will be:
[tex]6P + 6G[/tex]
Apply distributive property
[tex]6(P + G)[/tex]
Substitute values for P and G
[tex]6(4 + 3)[/tex]
Hence, the first option answers the question
What is 31 1/2 divided by 3 1/2
Answers
Answer:
9
Step-by-step explanation:
used a calculator
Please assist me with these problems and show the work. Part 1 4. From a horizontal distance of 80.0 m, the angle of elevation to the top of a fragpole is 18°. Calculate the height of the flagpole to the nearest tenth of a metre. 5. A 9.0 m ladder rests against the side of a wall. The bottom of the ladder is 1.5 m from the base of the wall. Determine the measure of the angle between the ladder and the ground, to the nearest degree.
Answers
Answer:
4) About 26.0 feet
5) About 80 degrees.
Step-by-step explanation:
Please refer to the (badly drawn, sorry) drawings.
4)
So for a horizontal distance of 80 meters, the angle of elevation is 18 degrees. And we want to find the height.
The horizontal distance is adjacent to the angle, and the height is opposite to the angle. Thus, we can use the trigonometric ratio tangent.
Recall that tangent is:
[tex]\tan(x)=opp/adj[/tex]
Substitute 18 for x, h for opposite, and 80 for adjacent. Thus:
[tex]\tan(18)=\frac{h}{80}[/tex]
To solve for h, multiply both sides by 80:
[tex]h=80\tan(18)[/tex]
Use a calculator:
[tex]h\approx25.9938[/tex]
So, the height is approximately 26.0 feet.
5)
So, this time, we need to find the angle. We know the hypotenuse and the side adjacent to the angle. So, we can use cosine. Recall that:
[tex]\cos(x)=adj/hyp[/tex]
Substitute 1.5 for adjacent and 9 for the hypotenuse. Thus:
[tex]\cos(x)=\frac{1.5}{9}[/tex]
Take the inverse cosine of both sides:
[tex]x=\cos^{-1}(\frac{1.5}{9})[/tex]
Use a calculator:
[tex]x\approx80.4059\textdegree\approx80\textdegree[/tex]
So, the angle is about 80 degrees.
And we're done!
Answer:
4) About 26.0 feet
5) About 80 degrees.
Step-by-step explanation:
how do i do linear functions?
Answers
Answer:
1. Substitute the value of f(x) into the problem. 8=3x-1.
2. Isolate the variable. Add 1 to both sides to isolate the variable term by using the opposite operation to move the constant term across the equal sign. ...
3. Continue to isolate the variable. ...
4. Simplify.
Step-by-step explanation:
the first term of an arithmetic sequence is equal to 200 and the common differencence is equal to -10. find the value of the 20th term
Answers
Answer:
The value for 20th term is 10.
Step-by-step explanation:
First, you have to find the formula for the sequence.
[tex]an = a + d(n - 1)[/tex]
[tex]let \: a = 200,d = - 10[/tex]
[tex]an = 200 - 10(n - 1)[/tex]
[tex]an = 200 - 10n + 10[/tex]
[tex]an = - 10n + 210[/tex]
Given that the formula of this sequence is an = -10n + 210. Next, you have to find 20th term :
[tex]let \:n = 20[/tex]
[tex]20th \: term = - 10(20) + 210[/tex]
[tex]20th \: term = - 200 + 210[/tex]
[tex]20th \: term = 10[/tex]
(Correct me if I am wrong)
Write an equation with a slope of -7 and a y-intercept of (0,4)
Answers
Answer:
Step-by-step explanation:
y - 4 = -7(x - 0)
y = -7x + 4
Can somebody help me pleaseeeee
Multiply -5/8•(-3)
Answers
Answer:3 [ 1 5 -5 6 0 0 ]
3 x 1 = 3
3 x 5 = 15
3 x -5 = -15
3 x 6 = 18
3 x 0 = 0
3 x 0 = 0
[ 3 15 -15 18 0 0 ]
[ 3 15 ]
[ -15 18 ]
[ 0 0]
The answer is B and I hope I explained this well for you
Step-by-step explanation:
Answer:
1.875
Step-by-step explanation:
you get out of school and walk orth for 20 minuties yo travel 1.6km what si the average velocity
Answers
Answer: The answer would be 1.6 :)
Answer:
The average velocity is:
4.8 km/hour
Step-by-step explanation:
1 hour = 60 minutes
20 minutes = 20/60 = 0.3333 hour
Proportions
1.6km ⇔ 0.3333 hour
W km ⇔ 1 hour
W = 1.6*1/0.3333
W = 4.8 km/hour
The sum of y and 13 divided by 2
Answers
Answer:
7.5
Step-by-step explanation:
Which explains a way the U.S. government has created incentives for people to save?
A. It has enforced regulations for product advertising and labeling.
B. It has established protections for monies placed into banks.
C. It has sued companies that make fraudulent claims to gain refunds.
D. It has worked to educate consumers about their responsibilities.
Answers
Answer: B
Step-by-step explanation: B. It has established protections for monies placed in banks
Give an answer to the picture above or below
Answers
Answer:
Graph
Step-by-step explanation:
The article ``Oxygen Consumption During Fire Suppression: Error of Heart Rate Estimation" reported the following data on oxygen consumption (ml/kg/min) for a sample of ten firefighters performing a fire suppression simulation:
29.5 49.3 30.6 28.2 28.0 26.3 33.9 29.4 23.5 31.6
Compute the following:
a. The sample range.
b. The sample variance s2 from the definition (i.e. first computing deviations, then squaring them, etc.).
c. The sample standard deviation.
d. s2 using the shortcut method.
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
29.5 49.3 30.6 28.2 28.0 26.3 33.9 29.4 23.5 31.6
Sort in ascending order of magnitude :
23.5,26.3,28.0,28.2,29.4,29.5,30.6,31.6,33.9,49.3
A) Range of the sample data:
(maximum - minimum)
49.3 - 23.5 = 25.8
B) sample variance :
S² = ∑ (x − m)²/ n − 1.
m = mean ; n = number of observations
m = (23.5 + 26.3 + 28.0 + 28.2 + 29.4 + 29.5 + 30.6 + 31.6 + 33.9 + 49.3) = 310.3 / 10 = 31.03
∑ (x − m)² = 443.801
n - 1 = 10 - 1 = 9
S² = ∑ (x − m)²/ n − 1
S² = 443.801 / 9
S² = 49.311222 = 49.31
C) The standard deviation (s):
S = √[∑ (x − m)²/ n − 1]
√variance = √49.311222
S = 7.0221949
S = 7.022
D) using statistical calculator,
S² = 49.31
Answer:
C
Step-by-step explanation:Hope this helps!:>
Resuelve las siguientes situaciones problemáticas: A) en una caja de 36 naranjas, si se han descompuesto, ¿qué parte del contenido de la caja se desperdicia? B) mi hermana hizo una pizza y la dividió en 8 porciones, si mi papá, mi hermano y mi tía comieron una porción cada uno, ¿qué la parte de la pizza queda?
Answers
Answer:
gdjlicnoirfbmlyrsrloydfbm
Tenemos dos problemas de proporciones.
Las soluciones son:
A) p = 6/36 = 1/6B) p = 5/8.A) Lamentablemente el primero está incompleto, lo reescribamos como:
"en una caja de 36 naranjas, si 6 se han descompuesto, ¿qué parte del contenido de la caja se desperdicia?"
Solo para mostrar la matemática que se necesita para este tipo de problemas.
La parte que del contenido de la caja que se desperdicia será igual al cociente entre el número de naranjas que se desperdician y el número total de naranjas, o sea:
p = 6/36 = 1/6
Se desperdicia 1/6 del contenido de la caja.
B) Sabemos que la pizza originalmente tiene 8 porciones.
Luego tu papá, hermano, y tía comen una porción (3 en total)
Entonces quedan: 8 - 3 = 5 porciones.
La parte que queda será el cociente entre lo que queda y la cantidad inicial, o sea:
p = 5/8.
Quedan 5/8 de la pizza.
Si quieres aprender más, puedes leer:
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Solve the formula 2x+3y=12 for y.
Answers
Answer:
y=4 - [tex]\frac{2x}{3}[/tex]
Step-by-step explanation:
The value of y for 2x + 3y = 12 is (12 - 2x) / 3.
Given,
2x + 3y = 12
We will solve for y.
How to solve an equation for a variable?We will keep the like terms on one side of the equation and solve for the required variable.
Example: x + 2x + y = 3 + 2y
Solve for y:
x + 2x + y = 3 + 2y
3x = 3 + 2y - y
3x - 3 = y
3(x - 1) = y
y = 3(x - 1) is our answer.
Solve 2x + 3y = 12 for y.
We have,
2x + 3y = 12
Keep y on one side of the equation.
3y = 12 - 2x
Divide both sides by 3.
y = (12 - 2x) / 3
Thus the value of y for 2x + 3y = 12 is (12 - 2x) / 3.
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A local pizza shop has a membership program for frequent buyers the membership cost $25 per month the members get a discount price of 150 per pizza slice Aaliyah purchased a membership to this pizza shop how much would a Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month what would be the monthly cost for a slice of pizza
Answers
This question was not written properly
Complete Question
A local pizza shop has a membership program for frequent buyers the membership cost $25 per month the members get a discount price of $1.50 per pizza slice. Aaliyah purchased a membership to this pizza shop , how much would Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month ?
What would be the monthly cost for a slice of pizza?
Answer:
a) $34
b) $26.50
Step-by-step explanation:
From the question:
Membership for frequent buyers in a month = $25
Discount price = $1.50 per pizza slice
a) How much would Aaliyah I have to pay the pizza shop if she bought six slices of pizza this month ?
This is calculated as:
Membership cost in a month + Discount price × Number of pizzas bought
= $25 +( $1.50 × 6 slices of pizza)
= $25 + $9
= $34
b) What would be the monthly cost for a slice of pizza?
This is calculated as:
Membership cost + Discount price × Number of slices
= $25 + $1.50 × 1
= $26.50
Solve for the variable!
1. 2x + 21 = 40
2. 4x - 12 = 3x + 9
3. 3(x -1) + 2 = 7x
Answers
Step-by-step explanation:
1. 2x + 21 = 40
2x = 40 - 21
2x = 19
x = 19/2 = 9.5
2. 4x - 12 = 3x + 9
4x - 3x = 9 + 12
x = 21
3. 3x - 3 + 2 = 7x
3x - 1 = 7x
-1 = 7x - 3x
-1 = 4x
4x = -1
x = -1/4
= - 0.25
Solve for x. −25x+175>225 AND 5x−83≥−73
Answers
Answer:
x < -2; x> or= 2
Step-by-step explanation:
-25x + 175>225
-25x>225-175
-25x>50
divide both sides by -25; we have
x <-2
the lesser than sign changes to a greater than because we are dividing by a negative number.
2. 5x - 83>_ -73
5x>_ -73 + 83
5x>_ 10
divide both sides by 5x we have
x>_ 2
Given 2x² = -8, x is
Answers
Answer:
its 2i or -2i
Step-by-step explanation:
just did it and also the next one is -4 and 10
Answer:
your answer will be "2i or -2i"
for the next it is -4 and 10
Step-by-step explanation:
There are two numbers which add up to 20. If one number is five more than four times the other, find the numbers.
Answers
Answer:
3 and 17
Step-by-step explanation:
Let x and y represent the numbers.
x + y = 20 . . . . . . . . the numbers add up to 20
x = 5 + 4y . . . . . . . . one number is 5 more than 4 times the other
Substituting the second equation into the first:
(5 +4y) +y = 20
5y = 15 . . . . . . . . . . subtract 5
y = 3 . . . . . . . . . . . . divide by 5
x = 20 -3 = 17
The numbers are 17 and 3.
find the inverse of the following function g(x) = -2x+3
Answers
Answer:
[tex]g(x)^-1 = \frac{-x}{2} +\frac{3}{2}[/tex]
Step-by-step explanation:
1) swap x and y
x = -2y + 3
2) solve for y
[tex]x=-2y+3[/tex]
[tex]2y=-x+3[/tex]
[tex]y=\frac{-x}{2} + \frac{3}{2}[/tex]
Answer:
[tex]\frac{y+3}{2}[/tex]
Step-by-step explanation:
Write the equation of the line in slope-intercept form.
Answers
y=mx+b
y=2x-7
Explanation
m = the “common difference” between two points
In this graph, it’s 2 because every time the line moves across the x axis by 1, it increases in 2 in the y axis
b = the point that intercepts the y axis; the y-intercept
In this graph, the point intercepts the y axis at -7 (the y-intercept is -7)
if 5a + 2b + 6c 32, what is the value of c?
Answers
Answer:
c= (-5a-2b+32)/6
Step-by-step explanation:
this is the answer, but you will b=have to a little more work to figure out each variable so you can get a number
Solve for x
9- 2y + 8y – 7 = -22
Answers
Answer:
-4
Step-by-step explanation:
-4
Step-by-step explanation:
Name the coordinate of P(-5, 8) under a translation along the
(x+2, y -1)
Answers
Explanation: the point (-5,8) moves to the left (x axis) 2 points and down (y axis) 1 point. Thus -5 + 2 = -3 and 8 - 1 = 7, so the answer is (-3, 7)
Determine the 3rd term in the geometric sequence whose first term is -8 & whose common term is 6
Answers
Answer:
so the formula for finding the n th term in a geometric sequence is :
(first term) * [tex](Common Term)^{n-1}[/tex]
therefore:
the 3 rd term will be
(-8) * (6)^2
-8 * 36
-288