a town has a population of 5000 and grows at 4% every year. what will be the population after 7 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.

Step2: Substitute the values

Given (P_0=5000), (r = 0.04) (since (4%=0.04)), and (t = 7). Substitute into the formula: (P=5000\times(1 + 0.04)^7). First, calculate ((1 + 0.04)^7). Using the formula ((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}) or a calculator, ((1.04)^7\approx1.315931779).

Step3: Calculate the population

Then (P=5000\times1.315931779). (P = 5000\times1.315931779=6579.658895).

Answer:

(6580)