law of exponential growth, y=ae bt where t is measured in days. If the population is 100 when t=0, and 300 when t=4. Find a and b.

Question

In a research experiment, a population of fruit flies is increasing according to the law of exponential growth, y=ae ^bt where t is measured in days. If the population is 100 when t=0, and 300 when t=4. Find a and b.

Answer 1

Hello, thank you for taking the time to post your question!

The variable “a” is actually given to us directly in the details of the question … it’s saying that the population is 100 when t = 0, meaning that a = 100

To find the value of “b” then you want to plug in what we know into the underlying exponential growth equation

300 = 100*e^(4b)

Solving that algebraically for the value of “b” using logarithms I get

3 = e^(4b)

ln(3) = 4b

b = ln(3) / 4 = 0.2747

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Hi Chris,

 

So here, y is the population, t is time and a and b are constants. So if we plug in 100 for the population and 0 for time, we can eliminate b and easily solve for a:

 

y = a*e^ (bt)

 

100 = a*e^(0)

 

100 = a * 1

 

a = 100

 

Next, use the value of a to solve for b with the second set of data:

 

300 = 100* e^(b*4)

3 = e ^(4b)

ln(3) = 4b

 

b = ln(3)/4

 

b = 0.275