the population of adamsville grew from 9000 to 13000 in 6 years. Assuming uninhibited exponential growth, what is the expected population in an additional 5 years?

Question

the population of adamsville grew from 9000 to 13000 in 6 years. Assuming uninhibited exponential growth, what is the expected population in an additional 5 years?

Answer 1

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

 

Since the population started at 9000 at t = 0 we have A = 9000 (since e⁰ = 1) 

 

Now use the given information (that the population was 13000 in 6 years) to figure out what k is equal to 

 

f(6) = 13000 = 9000e^k(6)  

13/9 = e6^k

ln(13/9) = 6k

6k = 0.36772478012

k = 0.06128746335

 

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

 

f(11) = 9000e¹¹⁽0.06128746335⁾ use calculator to find answer