The number of customers that visit a local small business is 51,200 and has been continuously declining at a rate of 3.8% each year. What is the approximate number of customers that visit the business in 14 years?
To find the approximate number of customers that will visit the business in 14 years, we need to calculate the future value of the declining number of customers.
Here is the step-by-step process to find the approximate number of customers:
1. First, calculate the annual decline rate: 3.8% = 0.038 (as a decimal).
2. Use the formula for compound interest:
Future Value = Present Value * (1 - Rate)^n
Where:
- Future Value is the number of customers after n years.
- Present Value is the initial number of customers (51,200).
- Rate is the annual decline rate (-0.038, since it's declining).
- n is the number of years (14).
3. Plug in the values into the formula:
Future Value = 51,200 * (1 - 0.038)^14
4. Calculate the expression inside the parentheses first:
(1 - 0.038)^14 ≈ 0.6069
Now, substitute this value back into the formula:
Future Value ≈ 51,200 * 0.6069
5. Calculate the result:
Future Value ≈ 31,047.68
Therefore, the approximate number of customers that will visit the business in 14 years is approximately 31,048.
(1-0.038)^14 * 51200 = roughly 29766.03373.....
So, since we cannot have 0.3373 customers, and because the question wants us to round, we get 29766 customers