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.

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Part 1
The number of employees in 11 years will be approximately

1 answer

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.