Question

A pair of athletic shoes costs $85. If the inflation rate remains constant at 9%, write an algebraic rule to determine the cost, c(t), of the

shoes after t years.
c(t) =
(Simplify your answer. Use integers or decimals for any numbers in the expression.)

Answer 1

c(t) = $85 × (1.09)^t

Explanation:

Assuming that the inflation rate remains constant at 9% per year, the cost of the athletic shoes after t years can be determined by multiplying the original cost by the inflation factor for t years, which is given by (1 + 0.09)^t, or 1.09^t. Therefore, the algebraic rule to determine the cost, c(t), of the shoes after t years is:

c(t) = $85 × 1.09^t

Simplifying the expression, we get:

c(t) = $85 × (1.09)^t

where t is the number of years after the original purchase.