Question

The number of employees for a certain company has been decreasing each year by 8​%. If the company currently has 700 employees and this rate​ continues, find the number of employees in 11 years.
Question content area bottom
Part 1
The number of employees in 11 years will be approximately

Answer 1

To calculate the number of employees in 11 years considering a decrease of 8% each year, we can use the formula for exponential decay:

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

where:
- \( N_0 \) is the current number of employees (700)
- \( r \) is the rate of decrease (0.08)
- \( t \) is the number of years (11)

Substituting the values into the formula:

\[
N = 700 \times (1 - 0.08)^{11}
\]

This simplifies to:

\[
N = 700 \times (0.92)^{11}
\]

Now, we can calculate \( (0.92)^{11} \):

\[
(0.92)^{11} \approx 0.2957
\]

Now, plug this value back into the equation:

\[
N \approx 700 \times 0.2957 \approx 207.0
\]

Thus, the number of employees in 11 years will be approximately \( 207 \) employees.