A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.
What is the surface area?Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.
Since we know the volume of the balloon, we can set up the following equation:
(4/3)πr^3 = 26*π ft^3
Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.
To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.
The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:
(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)
Plugging in the value of r that we found earlier (2.15 ft), we get:
(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min
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PLEASE PLEASE PLEASE HELP!!!
Sonya stopped at bakery A to buy 24 cookies. Bakery A sells 7 cookies for $5.60. On her way home, Sonya passed by another bakery B. Bakery B sells 5 cookies for $4.75. How much money did Sonya save by buying cookies at shop A? Please explain.
Answer:
$3.6 saved
Step-by-step explanation:
Shop A: -
7 cookies ----> $5.60
24 cookies -----> $x
x = (24 x 5.60) / 7
x = $19.2
Shop B: -
5 cookies ----> $4.75
24 cookies ---- > $y
y = (24 x 4.75) / 7
y = $22.8
Saved = Shop B - Shop A
Saved = 22.8 - 19.2
Saved = $3.6
I hope my answer helps you.
For the 2009 regular season, the MLB batting leaders in number of hits were Ichiro Suzuki and Derek Jeter. These two players had a total of 437 hits. Suzuki had 13 more hits than Jeter. How many hits did each player have?
Graph g(x) = −2x − 8 and identify its x-intercept.
(−8, 0)
(−4, 0)
(0, −4)
(0, −8)
Based on the graph of the function g(x) = −2x − 8, the x-intercept is equal to -4.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively.
What is the x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
By critically observing the graph of g(x) = −2x − 8, the x-intercept is -4. This ultimately implies that, the function g(x) = −2x − 8 would cross the x-coordinate (x-axis) at point (-4, 0.
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Find the volume of the composite solid
Find a positive and a negative coterminal angle for each given angle.
A positive and a negative co - terminal angle for each given angle is 1) -π/2 and -9π / 2 and 2) 7π / 2 and -π / 2 .
Given :
a positive and a negative co - terminal angle for each given angle
1 )
= -5π / 2
To find positive and negative co - terminal angle we need to add and subtract by 2π .
= -5π / 2 + 2π
= -5π + 4π / 2
= -π/2
= -5π / 2 - 2π
= -5π - 2 * 2π / 2
= -5π - 4π / 2
= -9π / 2
or =
2 )
= 3π / 2
= 3π / 2 + 2π
= 3π + 2 * 2π / 2
= 3π + 4π / 2
= 7π / 2
= 3π / 2 - 2π
= 3π - 4π / 2
= -π / 2
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a 50.0 cmcm, uniform, 50.0 nn shelf is supported horizontally by two vertical wires attached to the sloping ceiling (figure 1). a very small 20.0 nn tool is placed on the shelf midway between the points where the wires are attached to it.
the tension in each wire will be equal. The tension in each wire, T ,the tension in each wire is 85.36 N with its weight.
Assuming that the tool has negligible mass so that its weight does not contribute to the tension in the wires, the tension in each wire will be equal. The tension in each wire, T, can be calculated using the equation:
T = (W/2) + (L/2)*sin(θ),
where W is the weight of the shelf and L is the length of the shelf. The angle θ is the angle between the ceiling and the shelf.
In this case, W = 50 N, L = 50 cm and θ = 45°. Therefore, T = (50/2) + (50/2)*sin(45) = 50 + 35.36 = 85.36 N.
So, the tension in each wire is 85.36 N.
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The equation for line g can be written as y–1= – 1/10 (x+8). Parallel to line g is line h, which passes through the point ( – 5,5). What is the equation of line h?
Answer:
point-slope form: [tex]y+5=-\frac{1}{10}(x-5)[/tex]
slope-intercept form: [tex]y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Step-by-step explanation:
Point-Slope Form:We can express any one-variable linear equation as: [tex]y-y_1=m(x-x_1)[/tex], where "m" is the slope, and [tex](x_1, y_1)[/tex] is some point on the graph.
We're given the equation in point-slope form: [tex]y-1=-\frac{1}{10}(x+8)[/tex], and if we want to make a line parallel to this line, we just need the slopes to be the same. So let's just look at the value in front of the parenthesis. This is given to be: [tex]-\frac{1}{10}[/tex]
We can use this same form, to develop an equation parallel to the given line, and passing through: [tex](-5, 5)[/tex]
Plugging the values into the point-slope formula, we get:
[tex]y-(-5)=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}(x-5)[/tex]
From here we can also convert this into slope-intercept form, where "y" is isolated.
[tex]\\y+5=-\frac{1}{10}(x-5)\\\\y+5=-\frac{1}{10}x + \frac{5}{10}\\\\y + \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2}\\\\y + \frac{10}{2} - \frac{10}{2} = -\frac{1}{10}x + \frac{1}{2} - \frac{10}{2}\\\\y = -\frac{1}{10}x - \frac{9}{2}[/tex]
Find the value of x from the figure
Answer:
x = 20
Step-by-step explanation:
the figure is a parallelogram, therefore the sum of angle A and angle B is 180°, we solve with an equation
180 = 5x + 5 + 4x - 5
180 = 9x
x = 180 : 9
x = 20
------------------------
check
180 = 5x + 5 + 4x - 5
180 = 5 × 20 + 5 + 4 × 20 - 5 (remember PEMDAS)
180 = 180
the answer is good
Answer:
The angle x is equal to 20 degrees
Help pls I don’t understand
Step-by-step explanation:
QUESTION 3[tex]\triangle ABC[/tex] is inscribed in circle with centre O. OA, OB and OC are it's radii.Now, In [tex]\:\triangle AOB[/tex] and [tex]\:\triangle COB[/tex] [tex]OA\cong OC[/tex] (radii of same circle)[tex]\angle AOB \cong\angle COB[/tex] (Given)[tex]OB\cong OB[/tex] (common side)[tex] \rightarrow \:\red{\triangle AOB\cong \triangle COB}[/tex](By SAS congruence postulate)QUESTION 4In [tex]\:\triangle ABE [/tex] and [tex]\:\triangle CBE[/tex] [tex]AB\cong CB[/tex] (Given)[tex] \angle ABE \cong\angle CBE[/tex] (Given)[tex]BE\cong BE[/tex] (common side)[tex] \rightarrow \:\orange{\triangle ABE\cong \triangle CBE}[/tex](By SAS congruence postulate)The diagram below shows all the possible totals from adding together
the results of rolling two fair dice.
Calculate P(total is neither 5 nor 7).
Give your answer as a fraction in its simplest form.
Answer:
1/6
Step-by-step explanation:
ia fair dice only has 6 numbers so you can't get 7 so there is two 5 since its two fair dice it's out of 12,2/12 divide both by 2 because that the highest common factor and you get 1/6 that your answer
Suman has a piece of land, which is in the shape of a rhombus. She wants her two sons to work on the land and produce different crops. She divides the land in two equal parts by drawing a diagonal. If its perimeter is 400 m and one of the
diagonals is of length 120 m, how much area each of them will get for his crops ?
Please help me with the question along with steps.
Answer:
Step-by-step explanation:
Perimeter = 400
Diagonal= 120
Each Side= 400/4 = 100
Then, find the length of a straight line:
400= 120(2)+2x
400= 240+ 2x
400-240=2x
160=2x
x=80
Area of Triangle= 1/2(b)(h)
= 1/2(80)(120)
= 1/2(9600)
= 4800
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)
f(x, y) = x2y; x2 + 2y2 = 6
Refer to the photo taken.
A company shipped 3 boxes which each weighed 3.894 pounds and one box which weighed 6.7 pounds. What was the total weight of the 4 boxes?
The total weight of the 4 boxes was - 18.382 pounds.
A company shipped 3 boxes which each weighed 3.894 pounds.
As per the rule, we shall have to multiply the weight of the boxes of similar weight into 3 followed by the addition of the weight of the other box.
Then, we can get the final answer.
one box weighed = 3.894 pounds
Three boxes weighed = 3 * 3.894 pounds
= 11.682 pounds
Another box weighed = 6.7 pounds
The total weight of the 4 boxes was = ( 11.682 + 6.7 ) pounds
= 18.382 pounds
Hence, The total weight of the 4 boxes was - 18.382 pounds.
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Justin was out at a restaurant for dinner when the bill came. His dinner came to $35. After adding in a tip, before tax, he paid $44.10. Find the percent tip.
Justin paid a tip that was 26% of his bill.
Step-by-step explanation:1. Form the expression.[tex]\frac{44.10-35}{35}[/tex]
2. Calculate.[tex]\frac{44.10-35}{35}=0.26[/tex]
3. Conclude.Justin paid a tip that was 26% of his bill.
At a water park, 42 out of 56 tickets sold were child tickets. What percentage of the tickets
were child tickets?
Write your answer using a percent sign (96).
Answer:
75%
Step-by-step explanation:
42/56 * 100% = 0.75 * 100
= 75%
A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Celia and Felicity. Give an expression for each of the probabilities below as a function of n. Simplify your final expression as much as possible so that your answer does not include any expressions of the form (). (a) What is the probability that Celia is first in line? (b) What is the probability that Celia is first in line and Felicity is last in line? (C) What is the probability that Celia and Felicity are next to each other in the line? Feedback?
P = 1 / n (Celia is first and Felicity is last in line) (n - 1)
P (in the line, Celia and Felicity are next to one another) = 2/n
A class consists of n kids.
These n kids line up for recess.
Out of n kids, there are two kids named Celia and Felicity.
(b) There are n positions and n! ways for n youngsters to stand in a line.
Consequently, n is the entire number of possible situations!
Felicity is standing in the last position while Celia is in the first (fixed position)
The remaining (n - 2) children can stand in the remaining 8 (n - 2) positions! ways
As a result, Celia is first in line and Felicity is last in line for the number of favorable situations, which is (n - 2)!
P (Celia is first in line and Felicity is last in line) = [(n - 2)! / n!]
P = (n - 2)! / [n(n - 1)(n - 2)!]
P = 1 / n(n - 1)
The likelihood that Celia and Felicity are on the same row as one another.
Consider Celia and Felicity as a single student, then multiply by the number of pupils (n - 1)
One can arrange (n - 1) pupils in (n - 1) positions! ways
However, there are two methods to organize Celia and Felicity among themselves.
There are therefore 2 good reasons to put Celia and Felicity adjacent to each other (n - 1)!
P(Celia and Felicity in the line are next to one another) = 2! * (n - 1)! / n!
P = 2 * (n - 1)! / n (n - 1)
P = 2/n
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At a specific spot along the coast of North Carolina the continental shelf extensile 65 m from the shoreline into the ocean at that point the depth of the water is 85 m from there the ocean floor sloughs down to the ocean crust which begins 115 m from the show and I added depth of 2700 m find the slope of the ocean floor connecting the edge of the continental shelf in the beginning of the oceanic crust that section of the ocean floor is called the continental slope 
The continental slope of the ocean is given as follows:
-67.9.
How to calculate the slope?
The slope of an object or a situation is calculated by the division of the vertical change by the horizontal change.
The parameters for this problem are obtained as follows:
Horizontal change: 115 - 75 = 40 m.Vertical change = -(2800 - 85) = -2715 m, as the depth means that the height is negative relative to the surface, which is the sea level in this case.Then the slope of the ocean floor connecting the edge of the continental shelf in the beginning of the oceanic crust is calculated as follows:
m = -2715/40 = -67.9.
(division of the vertical change by the horizontal change obtained previously on this problem).
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√3ab
rewrite the equation in radical form
Answer:
√3√ab
Step-by-step explanation:
Please look in the attachment! Hope this helps! :D
1. Assume that there is a party consisting of people between the ages of 18 and 24 inclusive. How many people would have to be at the party to guarantee that at least three people share the same birth date, birth month, and birth year? Note: assume the range of birth years include 2 leap years. (10 points)
at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
To warrant that at least three people have the same date, month, and year of birth, we need to find the minimum number of people such that there is a probability that at least three people have the same date, month, and year. there is. Birth year she is 1 or more. Non-leap years have 365 days, and leap years have her 366 days. The birth year range includes two leap years, so there are 3652 + 3662 = 2,922 possible births. This means that the probability that a particular person's birthday is unique is (2922-1)÷2922 = 1÷2922.
Now we can use the birthday puzzle to calculate the probability that at least three people have the same birthday. The probability that no one has the same birthday is (1 - 1÷2922)^n, where n is the number of people in your party. At least he has 1-(1-1÷2922)^n probability that 3 of them have the same birthday. You can set this probability to 1 or more and solve for n.
1 - (1 - 1÷2922)^n >= 1
(1 - 1÷2922)^n <= 0
n >= log(0) ÷ log(1 - 1÷2922)
The logarithm of 0 is not defined, so you can use a small value on the right hand side instead. B. 10^-6. This will tell you:
n >= log(10^-6) ÷ log(1 - 1/2922)
n >= log(10^-6) ÷ log(2921/2922)
n >= log(10^-6) ÷ log(2921) - log(10^-6) / log(2922)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= log(10^-6) × log(2922) ÷ log(2921) - log(10^-6)
n >= 23.
Hence, at least 24 people must be in the party to guarantee that at least 3 people have the same date of birth, date of birth, date of birth.
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if angle GHJ is an equilateral triangle, GH = 5x - 13, HJ = 11x - 61, and GJ = 7x - 29, find x and the
measure of each side. Draw and label a picture and show all work for full credit. (10 pts)
Answer:
x is 8
And each side is 27
Step-by-step explanation:
check out the photo
hope it will help
$5400 is invested, part of it at 11% and part of it at 9%. For a certain year, the total
yield is $546.00. How much was invested at each rate?
Answer:$2400 invested at $9% $3000 invested at $11%
Step-by-step explanation:
the number of ants per acre in the forest is normally distributed with mean 45,000 and standard deviation 12,073. let x
There is a 32.81% chance (0.3182) that there will be between 32647 and 43559 ants on a randomly chosen acre.
How to calculate Z score?The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. We may calculate the likelihood that the value of the measure exceeds X by subtracting 1 from the pvalue.
The zscore of a measure X in a set with mean and standard deviation may be calculated as follows:
Z= X-μ/σ
μ = 42000 σ= 12275
The pvalue of Z when X = 32647 is deducted from the pvalue of Z when X = 43559 to get this value. So
X = 43559
z= 0.13 has a pvalue of 0.5517
X = 32647
z= -0.76 has a pvalue of 0.2236
0.5517 - 0.2236 = 0.3281
0.3182 = 32.81% probability that a randomly selected acre has between 32647 and 43559 ants.
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a sales manager analyzed the sales, in dollars, y, of snow shovels compared to the outside temperature, in degrees fahrenheit, x. the manager calculated the correlation coefficient of r
The correlation coefficient of r measures how closely the two variables, x and y, are related. If the coefficient is close to 1, it means that the two variables are strongly related, whereas if it is close to 0, it means that there is no relation between them.
The correlation coefficient of r is a measure of how closely related two variables are to each other. It is calculated by taking the covariance of the two variables and dividing it by the product of their standard deviations. The coefficient ranges from -1 to +1, with -1 indicating a perfectly negative linear relationship, 0 indicating no relationship, and +1 indicating a perfectly positive linear relationship. In the case of the sales manager analyzing the sales of snow shovels compared to the outside temperature, the correlation coefficient of r can be used to measure the strength of the relationship between the two variables. If the coefficient is close to 1, it indicates that the two variables are strongly related, while a coefficient close to 0 indicates that there is no relation between them.
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what is an expression equivalent to 5 1/4d - 5?
Answer:
Step-by-step explanation:
23
At the beginning of the year, Kaylee had $60 in savings and saved an additional $12 each week thereafter. Jack started the year with $95 and saved $5 every week. Let K represent the amount of money Kaylee has saved t weeks after the beginning of the year and let J represent the amount of money Jack has saved t weeks after the beginning of the year. Write an equation for each situation, in terms of t, and determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved.
After 5 week the savings of both Kaylee and Jack will be same.
The equation for Kaylee's savings, in terms of t, is K = 60 + 12t.
The equation for Jack's savings, in terms of t, is J = 95 + 5t.
To determine the number of weeks after the beginning of the year until Kaylee and Jack have the same amount of money saved, we set K equal to J and solve for t.
K = J
60 + 12t = 95 + 5t
7t = 35
t = 5
Kaylee and Jack have the same amount of money saved after 5 weeks.
What are savings?
The funds one has saved, particularly through a bank or government programme is known as savings.
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Find the circumference of a circle with a radius of 5 inches
Answer: The answer should be 31.42 in
Which sequence of transformations will change figure PQRS to figure P′Q′R′S′? (5 points)
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 180 degrees followed by reflection about the y-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the x-axis
Counterclockwise rotation about the origin by 270 degrees followed by reflection about the y-axis
The sequence of transformations to change figure PQRS to figure P′Q′R′S′ will be;
⇒ Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.
What is Translation?A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
Sequence of transformations will change figure PQRS to figure P′Q′R′S′.
Now,
Since, Sequence of transformations will change figure PQRS to figure P′Q′R′S′.
And, The coordinates of figure PQRS are,
P = (1, 2)
Q = (2, 1)
R = (3, 2)
S = (3, 3)
And, The coordinates of figure P'Q'R'S' are,
P' = (1, -2)
Q' = (2, -1)
R' = (3, -2)
S' = (3, -3)
We know that,
The transformation rule for Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis will be,
⇒ (x , y) → (x, - y)
Thus, We get;
The sequence of transformations to change figure PQRS to figure P′Q′R′S′ is,
''Counterclockwise rotation about the origin by 180 degrees followed by reflection about the x-axis.''
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: A cell phone manufacturer claims that the average battery life of its newest flagship smartphone is exactly 20 hours. Javier believes the population mean battery life is less than 20 hours. He tests this claim by selecting a random sample of 33 phones of this model. Javier found that the sample mean battery life is 19.5 hours with a sample standard deviation of 1.9 hours. Should Javier reject or fail to reject the null hypothesis given the sample data below? • H:u=20 versus H, u <20 . a=0.05 (significance level) . to = -1.51 • 0.05
There is not sufficient evidence to conclude that the population mean battery life is less than 20 hours, based on the sample data.
To test the null hypothesis, Javier can use a one-sample t-test. In this test, the null hypothesis is that the population mean is equal to the claimed value of 20 hours, and the alternative hypothesis is that the population mean is less than 20 hours. To determine whether to reject or fail to reject the null hypothesis, Javier can compare the t-statistic, calculated from the sample data, to the critical t-value at a significance level of 0.05. The critical t-value is the value beyond which the null hypothesis can be rejected.
In this case, the t-statistic is given as -1.51. To find the critical t-value, Javier can use a t-table or a statistical software package. At a significance level of 0.05 and a sample size of 33, the critical t-value is approximately -1.68. Since the t-statistic (-1.51) is less than the critical t-value (-1.68), Javier should fail to reject the null hypothesis.
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Talhah and Rosina are doing push ups for PE class. They both want to complete the same number of push ups, but Talhah wants to do 6 push ups per set and Rosina wants to do 8 push ups per set. After they finished they realized that while they did the same total number of push ups, Rosina needed 3 fewer sets to finish hers. How many push ups did each girl do?
The number of push ups done by each girl from the given parameters is; 72 push ups
How to solve Algebra Word Problems?We are given;
Rate of Push ups for Talhah = 6 push ups per set
Rate of Push ups for Rosina = 8 push ups per set
Let the number of sets of push ups done by each girl be denoted as x
Thus, since after they finished, they realized that while they did the same total number of push ups, Rosina needed 3 fewer sets to finish hers, then the equation here is;
6x = 8(x - 3)
Expanding the bracket gives;
6x = 8x - 24
8x - 6x = 24
2x = 24
x = 12 sets
Thus, number of push ups done by each = 6 * 12 = 72
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Describe the meanings of all the variables in the exponential functionQ=Q0 (1+r) t Explain how the function is used for exponential growth and decay. Choose the correct answer below. Select all that apply. A. The function is used for exponential growth if r<0B. The function is used for exponential decay if r>0C. The function is used for exponential growth if r>0D. The function is used for exponential decay if r<0.
The exponential function Q=Q0 (1+r) t can be used to describe exponential growth or decay depending on the value of r. If r is less than 0, the function can be used to describe exponential growth, whereas if r is greater than 0, the function can be used to describe exponential decay.
The exponential function Q=Q0 (1+r) t can be used to describe exponential growth or decay. The function is determined by three variables: Q0, which is the starting value of the function; r, which is the growth or decay rate of the function; and t, which is the time when the function occurs. If r is less than 0, then the function can be used to describe exponential growth, meaning that the output of the function will increase over time. On the other hand, if r is greater than 0, then the function can be used to describe exponential decay, meaning that the output of the function will decrease over time. The exponential function can be used to describe a variety of different processes, such as population growth, compound interest, and radioactive decay. It can also be used to predict future values based on past values by using the growth or decay rate. Thus, the exponential function is a powerful tool for describing and predicting exponential growth and decay.
Q=Q0 (1+r) t
For example, if Q0 = 10, r = 0.5, and t = 5, then
Q=10 (1+0.5)5
Q= 10 x 1.53
Q= 15.3
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