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

Answer:

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

$B)8688\text{ persons}$

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                            $7652\times (1.016)^t$

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:

$P(8)=7652\times (1.016)^{t}=7652(1.016)^{8}=8688.09628\approx 8688$