question\na town has a population of 13000 and grows at 4.5% every year. what will be the population after…

question\na town has a population of 13000 and grows at 4.5% every year. what will be the population after 13 years, to the nearest whole number?

question\na town has a population of 13000 and grows at 4.5% every year. what will be the population after 13 years, to the nearest whole number?

Answer

Explanation:

Step1: Use the compound - growth 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. Given (P_0=13000), (r = 0.045) (since (4.5%=0.045)), and (t = 13).

Step2: Substitute the values into the formula

[ \begin{align*} P&=13000\times(1 + 0.045)^{13}\ &=13000\times(1.045)^{13} \end{align*} ] First, calculate ((1.045)^{13}). Using a calculator, ((1.045)^{13}\approx1.763273).

Step3: Calculate the final population

[ \begin{align*} P&=13000\times1.763273\ &=22922.549 \end{align*} ]

Answer:

(22923)