1. The population of a town was 5655 in 2010. The population grows at a rate of 1.4% annually. (a) Use the exponential growth model to write an equation that estimates the population t years after 2010. (a) Estimate the population of the town in 2022. Show your work.

Answers

Answer 1

(a) The exponential growth model is P = 5655 e^(0.014t)

(b) Population of the town in 2022 is 6689.5065.

What is Population Growth?

Population growth is defined as the number of people increasing over years in a specific region calculated using annual growth rate.

(a) The formula to calculate population growth is,

P = P₀ e^(r t)

Given,

Initial population in 2010, P₀ = 5655

Annual growth rate, r = 1.4% = 0.014

Substituting,

P = 5655 e^(0.014t)

(b) To estimate the population of town in 2022,

t = 2022 - 2010 = 12 years

Substituting value of t in the formula in (a),

P = 5655 e^(0.014 × 12)

= 5655 e^(0.168)

= 5655 × 1.1829

= 6689.5065

Hence the population is 6689.5065 in 2022.

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Step-by-step explanation:

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