Question

a town has a population of 17000 and grows at 3% every year. what will be the population after 10 years, to the nearest whole number?

Explanation:

Step 1: 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 annual growth rate (as a decimal), and $t$ is the number of years.
Here, $P_0 = 17000$, $r = 0.03$ (since 3% = 3/100 = 0.03), and $t = 10$.

Step 2: Substitute the values into the formula

Substitute the given values into the formula: $P(10) = 17000(1 + 0.03)^{10}$.

Step 3: Calculate $(1 + 0.03)^{10}$

First, calculate $(1.03)^{10}$. Using a calculator, $(1.03)^{10} \approx 1.343916379$.

Step 4: Multiply by the initial population

Now, multiply this by the initial population: $P(10) = 17000 \times 1.343916379$.

Calculate this product: $17000 \times 1.343916379 \approx 22846.57844$.

Step 5: Round to the nearest whole number

Rounding $22846.57844$ to the nearest whole number gives 22847.

Answer:

22847