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.