Question

The population of a town was 7652 in 2016. The population grows at a rate of 1.6% annually.

(A) use the exponential growth model to write an equation that estimate the population t years after 2016.
(b) estimate the population in 2024. Show work

Answer 1

`A) P(t)=7652(1.016)^t`

`B)8688\text{ persons}`

Step-by-step explanation:

(A) Use the exponential growth model to write an equation that estimate the population t years after 2016

Calculating some terms will help you to determine the exponential growth model to estimate the population t years after 2016.

Year Number of years Population

after 2016 P(t)

2016 0 7652

2017 1 7652 + 7652 × 0.016 = 7652 × (1.016)

2018 2 7652 × (1.016)²

2019 3 7652 × (1.016)³

t
`7652* (1.016)^t`

Hence the equation that estimates the population t years after 2016 is:

`P(t)=7652(1.016)^t`

(B) Estimate the population in 2024.

Year 2024 is 2024 - 2016 = 8 years after 2016. Hence, t = 8 years and you just must substitute t with 8 in the model (equation) to estimate the population in year 2024:

`P(8)=7652* (1.016)^(t)=7652(1.016)^(8)=8688.09628\approx 8688`