9. Story problem.

Question

9. The population of a city is increasing at a rate proportional to its size. It follows the function P(t)=1+ke0.03t where k is constant and t is the time in years. If the current population is 18,000, in how many years is the population expected to be 45,000?

Answer 1

I assume the correct function is

 

P(t) = P(0)e^0.03t

 

P(0) = 18,000

 

P(t) = 18,000e^0.03t

 

Set P(t) = 45,000 and solve for t.

 

45,000 = 18,000e^0.03t

 

2.5 = e^0.03t

 

0.03t = ln2.5

 

t = ln2.5 / 0.03 years ≅ 30.54 years

 

Test the answer.