Final answer:
To calculate the number of employees in 10 years given a 6% annual decrease, we use the formula for exponential decay. With a current count of 680 employees, the calculation shows there will be approximately 367 employees after 10 years.
Step-by-step explanation:
The question you asked pertains to exponential decay, which is a concept in mathematics that describes the process of a quantity decreasing at a rate proportional to its current value. In this case, the quantity is the number of employees at a company, and the rate of decrease is 6% per year. To find the number of employees in 10 years, we need to apply the formula for exponential decay:
N(t) = N0 * (1 - r)^t
Where:
- N(t) is the number of employees at time t,
- N0 is the current number of employees,
- r is the rate of decrease (expressed as a decimal), and
- t is the time in years.
Plugging in the values we have:
N(10) = 680 * (1 - 0.06)^10
After doing the calculations:
N(10) = 680 * 0.5394
N(10) = 366.792 employees
After rounding to the nearest whole number, the company would have approximately 367 employees in 10 years if the current rate of decrease continues.