a town has a population of 10000 and grows at 5% every year. what will be the population after 5 years, to…

a town has a population of 10000 and grows at 5% every year. what will be the population after 5 years, to the nearest whole number?

a town has a population of 10000 and grows at 5% every year. what will be the population after 5 years, to the nearest whole number?

Answer

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 as a decimal, and (t) is the time in years.

Step2: Substitute the values

Given (P_0=10000), (r = 0.05) (since (5%=0.05)), and (t = 5). Substitute into the formula: (P=10000\times(1 + 0.05)^5).

Step3: Calculate ((1 + 0.05)^5)

((1+0.05)^5=1.05^5). Using a calculator, (1.05^5=1.05\times1.05\times1.05\times1.05\times1.05 = 1.27628).

Step4: Calculate (P)

(P = 10000\times1.27628=12762.8).

Answer:

(12763)