Question

the number of employees for a certain company has been decreasing each year by 8%. if the company currently has 530 employees and this rate continues, find the number of employees in 13 years. (round to the nearest whole number as needed) the number of employees in 13 years will be approximately 178

Explanation:

Step1: Identify the formula for exponential decay

The formula for exponential decay is $A = P(1 - r)^t$, where $A$ is the final amount, $P$ is the initial amount, $r$ is the rate of decay (as a decimal), and $t$ is the time in years.

Step2: Plug in the given values

Here, $P = 530$, $r = 0.08$ (since 8% = 0.08), and $t = 13$. So we have $A = 530(1 - 0.08)^{13}$.

Step3: Calculate $(1 - 0.08)$

$1 - 0.08 = 0.92$. So now the formula becomes $A = 530(0.92)^{13}$.

Step4: Calculate $(0.92)^{13}$

Using a calculator, $(0.92)^{13} \approx 0.3358$.

Step5: Multiply by the initial amount

$A = 530 \times 0.3358 \approx 178$.

Answer:

178