Question

somerville has a population of 38,400 people. the town has been seeing its population decline by 3% every year. if this trend continues, what will the population be in 3 years? if necessary, round your answer to the nearest whole number. people submit

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $P(t) = P_0(1 - r)^t$, where $P_0$ is the initial population, $r$ is the rate of decay (as a decimal), and $t$ is the time in years.
Here, $P_0 = 38400$, $r = 0.03$ (since 3% = 0.03), and $t = 3$.

Step2: Substitute the values into the formula

Substitute $P_0 = 38400$, $r = 0.03$, and $t = 3$ into the formula:
$P(3) = 38400(1 - 0.03)^3$

Step3: Simplify the expression inside the parentheses

First, calculate $1 - 0.03 = 0.97$. So the formula becomes $P(3) = 38400(0.97)^3$.

Step4: Calculate $(0.97)^3$

Calculate $0.97^3 = 0.97\times0.97\times0.97 = 0.912673$.

Step5: Multiply by the initial population

Now, multiply $38400$ by $0.912673$:
$38400\times0.912673 = 38400\times0.912673 \approx 35046.6432$.

Step6: Round to the nearest whole number

Rounding $35046.6432$ to the nearest whole number gives $35047$.

Answer:

35047