Exponential growth of fruit flies

Question

Suppose an experimental population of fruit flies increases according to the law of exponential growth. There were 100 flies at the end of the second day of the experiment and 300 flies at the end of the fourth day.
A) Find an equation that models the number of flies y after at the end of the t days.



B) Approximately how many flies were in the population at the start ?


C) Approximately how many flies are there after 10 days ?

Answer 1

Y= ce^kt

Sub in 300= ce^4k

100= ce^2k

Divide to get 3= e^2k

Take log of both sides    ln3= 2k lne

So k=ln3/2

 

We now have y=ce^(ln3/2)t

Sub in to solve for t

100= ce^ln3

c=100/3

A Equation is y=100/3 e^(ln3/2) t

B At t=0 there were approx 100/3 or 33 filies.

C After 10 days there will be 100/3 e^(ln3)/2 *10 or approx  8100 flies.