Question

pair of athletic shoes costs ​105$. If the inflation rate remains constant at 7​%, write an algebraic rule to determine the​ cost, c(t), of the shoes after t years.

Answer 1

c(t) = 105·1.07^t

Explanation:

You want an exponential equation describing the cost of athletic shoes that are $105 now and whose cost is growing at 7% per year for t years.

Exponential equation

The general form of the exponential equation is ...

c(t) = a·b^t

where 'a' is the initial cost (105) and b is the growth factor. The growth factor is related to the given growth rate by ...

b = 1 +r = 1 +7% = 1.07

Then the equation is ...

c(t) = 105·1.07^t