Question

a town has a population of 5000 and grows at 4% every year. what will be the population after 7 years, to the nearest whole number?

Explanation:

Step1: Recall the compound growth formula

The formula for compound growth is $P(t) = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the growth rate (in decimal), and $t$ is the time in years.
Here, $P_0 = 5000$, $r = 0.04$ (since 4% = 0.04), and $t = 7$.

Step2: Substitute the values into the formula

Substitute $P_0 = 5000$, $r = 0.04$, and $t = 7$ into $P(t) = P_0(1 + r)^t$:
$P(7) = 5000(1 + 0.04)^7$
First, calculate $(1 + 0.04) = 1.04$. Then, calculate $1.04^7$. Using a calculator, $1.04^7 \approx 1.315931779$.

Step3: Calculate the final population

Multiply 5000 by $1.315931779$:
$P(7) = 5000 \times 1.315931779 \approx 6579.658895$

Step4: Round to the nearest whole number

Rounding $6579.658895$ to the nearest whole number gives 6580.

Answer:

6580