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 18 years.


To solve this problem, we need to use the formula for exponential decay:

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

Where:
- \( N(t) \) is the number of employees after \( t \) years,
- \( N_0 \) is the initial number of employees,
- \( r \) is the rate of decrease (in decimal form),
- \( t \) is the time in years.

Here:
- \( N_0 = 560 \) (initial number of employees),
- \( r = 8\% = 0.08 \),
- \( t = 18 \) years.

Now we can plug in the values:

\[
N(18) = 560 \times (1 - 0.08)^{18}
\]
\[
N(18) = 560 \times (0.92)^{18}
\]

Let me calculate that for you.The number of employees in 18 years will be approximately 125 if the current 8% annual decrease continues.

Would you like more details or have any questions?

Here are five related questions to consider:
1. How would the result change if the rate of decrease was 10% instead of 8%?
2. What would be the number of employees after 10 years instead of 18 years?
3. How can we calculate the time it would take for the company to have fewer than 50 employees?
4. How can this model be applied to other scenarios, like population decline?
5. What happens if the rate of decrease fluctuates instead of remaining constant?

**Tip:** Exponential decay processes, like this one, are common in finance, physics, and population studies, as they model gradual reduction over time.

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 18 years.

Learn how to calculate the number of employees in a company after 18 years, given an 8% annual decrease. This problem covers exponential decay concepts and percentage decrease, suitable for Grades 9-12 students.

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