a town has a population of 14000 and grows at 5% every year. what will be the population after 14 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 as a decimal, and (t) is the time in years. Here, (P_0=14000), (r = 0.05), and (t = 14).

Step2: Substitute the values into the formula

Substitute the values into the formula: (P=14000\times(1 + 0.05)^{14}). First, calculate ((1 + 0.05)^{14}). Using the formula (a^n=e^{n\ln(a)}), ((1.05)^{14}=e^{14\ln(1.05)}). (\ln(1.05)\approx0.04879), then (14\ln(1.05)=14\times0.04879 = 0.68306). (e^{0.68306}\approx1.98979). Or, using a calculator directly, ((1.05)^{14}\approx1.97993). Then (P = 14000\times1.97993).

Step3: Calculate the final population

(P=14000\times1.97993=27719.02)

Answer:

(27719)