Question

question a town has a population of 7000 and grows at 4% every year. what will be the population after 13 years, to the nearest whole number? answer attempt 1 out of 3

Explanation:

Step1: Identify the formula for compound growth

The formula for compound growth is $P = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the growth rate per year, and $t$ is the number of years.
Here, $P_0 = 7000$, $r = 0.04$ (since 4% = 0.04), and $t = 13$.

Step2: Substitute the values into the formula

Substitute $P_0 = 7000$, $r = 0.04$, and $t = 13$ into the formula:
$P = 7000(1 + 0.04)^{13}$

Step3: Calculate $(1 + 0.04)^{13}$

First, calculate $1 + 0.04 = 1.04$. Then, find $1.04^{13}$. Using a calculator, $1.04^{13} \approx 1.66507$.

Step4: Calculate the population $P$

Multiply $7000$ by $1.66507$:
$P = 7000 \times 1.66507 \approx 11655.49$

Step5: Round to the nearest whole number

Rounding $11655.49$ to the nearest whole number gives $11655$.

Answer:

11655