Question

Mrs. Smith and her daughter Laura want to learn ballet. The cost of beginning ballet classes for kids is $3,200 per year, and it increases by 2% every year. The cost of beginning ballet classes for adults is $4,800 per year, and it increases by 2.7% per year. Which function can Mrs. Smith use to determine the total cost of their ballet classes, T(x), after x years?

Answer 1

We will set up two functions to begin with: C(x) for children and A(x) for adults. T(x) will be the total, and T(x) = C(x) + A(x).
Since it increases by a percentage every year we will use an exponential function.
C(x) = 3200(1+0.02)ˣ. This comes from the $3200 for the first year, and 2% increase every year is 0.02. Add this to 1 because we have all of the first year's cost, 100%, and the additional 2%.
A(x) = 4800(1+0.027)ˣ. This comes from the $4800 for the first year, and 2.7% increase every year is 0.027. Add this to 1 because we have 100% of the first year's cost with an additional 2.7%.
T(x) = 3200(1+0.02)ˣ+4800(1+0.027)ˣ=3200(1.02)ˣ+4800(1.027)ˣ