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The number of employees for a certain company has been decreasing each year by 4​%. If the company currently has 740 employees and this rate​ continues, find the number of employees in 19 years.

User JayKan
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Final answer:

To calculate the number of employees a company will have in 19 years given a 4% yearly decrease, use the exponential decay formula N = N0 * (1 - r)^t. For the company with 740 current employees, it is expected to have approximately 331 employees in 19 years.

Step-by-step explanation:

The question is asking how to calculate the future number of employees of a company given a constant rate of decrease. To solve this, we need to use the formula for exponential decay, which fits this scenario because the company's employee count decreases by a constant rate each year. The formula is:

N = N0 * (1 - r)^t

Where N is the future number of employees, N0 is the current number of employees, r is the rate of decrease (expressed as a decimal), and t is the number of years. In this case, with 740 employees currently, a 4% annual decrease, and looking 19 years into the future, the calculation is:

N = 740 * (1 - 0.04)^19

Calculating this gives us:

N = 740 * 0.4478...

N ≈ 331.2

Therefore, in 19 years, the company is expected to have approximately 331 employees if the current rate of decrease continues.

User Altro
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