Question

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Part 1
The number of employees for a certain company has been decreasing each year by 8​%. If the company currently has 560 employees and this rate​ continues, find the number of employees in 15 years.
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Part 1
The number of employees in 15 years will be approximately
  
enter your response here.
​(Round to the nearest whole number as​ needed.)

Answer 1

To find the number of employees in 15 years given a yearly decrease of 8%, we can use the formula for exponential decay:

\[
N = N_0 \times (1 - r)^t
\]

where:
- \(N\) is the number of employees after \(t\) years,
- \(N_0\) is the current number of employees,
- \(r\) is the rate of decrease,
- \(t\) is the number of years.

Given:
- \(N_0 = 560\),
- \(r = 0.08\),
- \(t = 15\).

Plugging these values into the formula:

\[
N = 560 \times (1 - 0.08)^{15}
\]
\[
N = 560 \times (0.92)^{15}
\]

Now, calculate \(0.92^{15}\):

\[
0.92^{15} \approx 0.2675
\]

Now multiply this value by 560:

\[
N \approx 560 \times 0.2675 \approx 149.8
\]

Rounding to the nearest whole number, the number of employees in 15 years will be approximately:

\[
\boxed{150}
\]