a town has a population of 5000 and grows at 2% every year. what will be the population after 5 years, to…

Explanation:

Step1: Identify the formula

The formula for compound - growth is (P = P_0(1 + r)^t), where (P_0) is the initial population, (r) is the growth rate, and (t) is the time.

Step2: Substitute the values

Given (P_0=5000), (r = 0.02) (since (2%=0.02)), and (t = 5). Substitute into the formula: (P=5000\times(1 + 0.02)^5).

Step3: Calculate ((1 + 0.02)^5)

((1+0.02)^5=1.02^5). Using the formula (a^n=\underbrace{a\times a\times\cdots\times a}_{n\text{ times}}), (1.02^5=1.02\times1.02\times1.02\times1.02\times1.02 = 1.1040808032).

Step4: Calculate (P)

(P = 5000\times1.1040808032). (P=5520.404016).

Answer:

(5520)