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?
customers in 14 years = 51,200 (1-0.038)^14
Did they give you a formula for this?
To find the approximate number of customers that will visit the business in 14 years, we can use the formula for exponential decay:
N = N0 * (1 - r)^t
where:
N is the current number of customers (51,200)
N0 is the initial number of customers
r is the rate of decline (3.8% = 0.038)
t is the number of years (14)
Let's substitute the values into the formula and calculate:
N = 51,200 * (1 - 0.038)^14
To simplify, we can calculate (1 - 0.038)^14 as a decimal value:
(1 - 0.038)^14 ≈ 0.591607
Now, we can substitute this value back into the formula:
N ≈ 51,200 * 0.591607
Calculating this expression:
N ≈ 30,288.4864
Therefore, the approximate number of customers that will visit the business in 14 years is 30,288.