The population grew from 8000 to 15000 in 8 years. Assuming uninhibited exponential growth, what is the expected population in an additional 2 years

Question

The population grew from 8000 to 15000 in 8 years. Assuming uninhibited exponential growth, what is the expected population in an additional 2 years?

Answer 1

The formula for exponential growth is  f(t) = Ae^kt  

 

Since the population started at 8000 at t = 0 we have A = 8000 (since e⁰ = 1)  

 

Now use the given information (that the population was 15000 in 8 years) to figure out what k is equal to  

 

f(8) = 15000 = 8000e^k(8)  

15/8 = e^8k

ln(15/8) = 8k

8k = 0.628608659

k = 0.078576082  

 

Now use this value of k to evaluate f when t = 10 in an additional 2 years  

 

f(10) = 8000e^{10(0.078576082)} ~ 17553