Question

The population of a city is described with the following function:P(t) = 65,000e 081Where P(t) is people in the city and t is time in years after 2000,Describe what is happening to this city, is it increasing or decreasing? By how much. Whatshould the population be in the year 2020?

Answer 1

Check Explanation

Step-by-step explanation

The population of the city is given as

P(t) = 65,000 e⁻.⁰⁸ᵗ

We are asked to determine if the population of the city is increasing or decreasing

To do this, we check the population as time progresses to see the pattern.

In 2000, t = 0

P(t) = 65,000 e⁻.⁰⁸ᵗ

P(0) = 65,000

In 2001, t = 1

P(t) = 65,000 e⁻.⁰⁸ᵗ

P(1) = 65,000 e⁻.⁰⁸ = 65,000 (0.9231) = 60,0003

In 2002, t = 2

P(t) = 65,000 e⁻.⁰⁸ᵗ

P(2) = 65,000 e⁻.¹⁶ = 65000 (0.9231)² = 65,000 (0.8521) = 55,387

It is obvious that the population of the city is decreasing and we can see that the population the next year is only about 92.31% (e⁻.⁰⁸) of the previous year, so, we can say that the population of the town is decreasing by 7.69% (100% - 92.31%) every year.

In 2020, t = 20

P(t) = 65,000 e⁻.⁰⁸ᵗ

P(20) = 65,000 e⁻¹.⁶ = 65,000 (0.9231)²⁰ = 65,000 (0.2019) = 13,123

Hope this Helps!!!