due to its weakening steel industry, clay county has been experiencing population decline of 3% every year…

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

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

Answer

Explanation:

Step1: Identify the formula

The formula for exponential - decay is $P = P_0(1 - r)^t$, where $P_0$ is the initial population, $r$ is the rate of decay, and $t$ is the time in years.

Step2: Substitute the given values

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

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

$(1 - 0.03)^{10}=0.97^{10}$. Using a calculator, $0.97^{10}\approx0.737424$.

Step4: Calculate the final population

$P = 10300\times0.737424\approx7595$.

Answer:

7595