Question

a town???s population increased from 175 000 to 262 500 in a decade. what is the average percent increase of population per year?

Answer 1

A decade is a period of 10 years.

The population increase for the 10 years can be modeled using the following population model.

N(t) = N₀eˣᵃ

Where :

N(a) = population at time a

N₀ = initial population

x = population growth rate

a = time

In our case :

N(10) = 262500

N₀ = 175000

a = 10
Doing the substitution we have :

262500 = 175000e¹⁰ˣ

262500/175000 = e¹⁰ˣ

1.5 = e¹⁰ˣ

Taking ln on both sides we have :

0.4055 = 10x

X = 0.04055

= 4.055%