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?

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