Question

exponential functions - basic
score: 0/5 penalty: 0.5 off
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?
answer

Explanation:

Step1: Recall exponential growth formula

The formula for exponential 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.

Step2: Identify values

Here, $P_0 = 17000$, $r = 0.03$ (since 3% = 0.03), and $t = 10$.

Step3: Substitute into formula

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

Step4: Calculate $(1 + 0.03)^{10}$

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

Step5: Multiply by initial population

Multiply this by 17000: $17000 \times 1.343916379 \approx 22846.57844$.

Step6: Round to nearest whole number

Rounding 22846.57844 to the nearest whole number gives 22847.

Answer:

22847