How do I solve this question?

Question

The population (p) (in thousands) of a city increase a time (t) (yrs) follows the exponential growth equation n(p)=432e0.025t. How long will it take for the population to reach 650,000?

Answer 1

This question relies on our understanding of the exponential growth function, and our ability to invert it.

We are given the equation p=432e^0.025t and we are told to find t when p= 650000

We substitute our value for p, giving us 650000=432e^0.025t We then solve for t using the steps below

650000=432e^0.025t

(650000/432)=e^0.025t

ln(650000/432)=ln(e^0.025t)=0.025t ln and e cancel out here

ln(650000/432)/(0.025)=t=292.65

We expect it will take 292.65 years for the population to grow to 650,000 people