Question

38 the population of a town is 12, 000, and it grows at a rate of 5% per year. what will the population be in 4 years?
a about 12, 600
b about 14, 420
c about 14, 586
d about 56, 401

Explanation:

Step1: Recall compound growth formula

The formula for compound population growth is $P = P_0(1 + r)^t$, where $P_0$ is initial population, $r$ is annual growth rate, $t$ is time in years.

Step2: Identify given values

$P_0 = 12000$, $r = 0.05$, $t = 4$

Step3: Substitute values into formula

$P = 12000(1 + 0.05)^4$

Step4: Calculate the growth factor

First compute $(1.05)^4 = 1.05\times1.05\times1.05\times1.05 = 1.21550625$

Step5: Compute final population

$P = 12000\times1.21550625 = 14586.075$

Answer:

C. about 14,586