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?

T(x) = 1,600[2(1.27)x + 3(1.2)x]

T(x) = 1,400[2(1.2)x + 3(1.27)x]

T(x) = 1,400[2(1.027)x + 3(1.02)x]

T(x) = 1,600[2(1.02)x + 3(1.027)x]

Answer 1

Correct Answer: Fourth Option

The total cost is the sum of cost of Ballet Classes for kids and cost of Ballet classes for adults.

For Kids:
The cost is $3200 and is increases at a rate of 2% every year. So the cost after x years can be expressed as:

$T_{kids}=3200(1.02)^{x}$

For adults:
The cost is $4800 and is increases at a rate of 2.7% every year. So the cost after x years can be expressed as:

$T_{adults}=4800(1.027)^{x}$

Total cost is the sum of these two costs. So,

$T(x)=3200(1.02)^{x}+4800(1.027)^{x} \\ \\ T(x)=1600[2(1.02)^{x}+3(1.027)^{x} ]$

Therefore, Fourth option is the correct answer.