Question

A landscaping company sees that the number of customers increases by 12% each month. If the company has 68 customers when it opens, which function, f(x), models the number of customers in the \displaystyle x^{th}x th month?

Answer 1

f(x) = 1.12 * f(x-1) (number of customers in the x-th month)

Explanation:

The number of customers is increasing by 12% each month, which means that the number of customers in the next month will be 100% + 12% = 112% = 1.12 times the number of customers in the current month.

If we let f(x) be the number of customers in the x-th month, and assuming that the company has 68 customers when it opens, we can write:

f(1) = 68 (number of customers in the first month)

f(2) = 1.12 * f(1) (number of customers in the second month)

f(3) = 1.12 * f(2) (number of customers in the third month)

f(4) = 1.12 * f(3) (number of customers in the fourth month)

...

f(x) = 1.12 * f(x-1) (number of customers in the x-th month)

This recursive formula shows that the number of customers in each month is 1.12 times the number of customers in the previous month.