# CALCULUS QUESTION?

Hi! I've been stuck on this calculus problem for 30+ minutes. I need to know how it is solved, it's killing me. The question is as follows:

The population of a certain city, which was 20,000 on January 1 of 1975, decreases exponentially with a decay constant of 0.4 When was the population declining by 1000 people per year?

The answer is 5.1986 years.

I'm confused on how to work backwards and get the correct answer for t. t being years after 1975.

### 1 Answer

Relevance

- alexLv 74 weeks ago
rule

P = 20000 e^(-0.4t)

dP/dt=-8000 e^(-0.4t)

the population declining by 1000 people per year --> dP/dt=-1000

-8000 e^(-0.4t) =-1000

solve for t

-->t = 5.1986 years

---> t =

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