Question

due to its weakening steel industry, clay county has been experiencing population decline of 3% every year. the current population is 10,300 people. assuming the trend continues, what will the population be in 10 years?
if necessary, round your answer to the nearest whole number.
people
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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.

Step2: Plug in the given values

Here, $P_0 = 10300$, $r = 0.03$ (since 3% = 0.03), and $t = 10$. So we have $P(10) = 10300(1 - 0.03)^{10}$.

Step3: Calculate $(1 - 0.03)^{10}$

First, calculate $1 - 0.03 = 0.97$. Then, $0.97^{10} \approx 0.7374$.

Step4: Multiply by the initial population

Multiply $10300$ by $0.7374$: $10300 \times 0.7374 \approx 7595.22$.

Step5: Round to the nearest whole number

Rounding $7595.22$ to the nearest whole number gives $7595$.

Answer:

7595