The tuition at a public university was $21,000 in 2008.

Question

The tuition at a public university was $21,000 in 2008. Between 2008 and 2010, the tuition had increased by 15%. Since then, it has continued to grow exponentially. Select all statements that describe the growth in tuition cost.

a. The tuition can be defined by the function f(y)=21,000∗(.5)^x/2=21,000∗(1.15)^x/2, where x represents years since 2008.

b. The tuition cost increased about 7.5% each year.

c. The tuition cost increased about 7.2% each year.

d. The tuition cost roughly doubles in 10 years.

e. The tuition cost can be approximated by the function f(d)=21,000∗2^d, where d represents decades since 2008.

I think the answers are a, c, d, & e but I want to make sure about reasoning.

Answer 1

1.15 = e^2r

r=ln(1.15)/2

e^ln(1.15)x/2 = (1.15)^x/2

Statement a is not real clear, should be f(x), not f(y).

f(x) = 21000(1.15)^t/2

Not sure why 2100(.5)^x/2 is in the middle of that equation.

f(1) =21000√1.15 ≈ 21000(1.072) = 21000(1 + 0.072) --> 7.2% increase

So statement b is false and c is true.

f(10) = 21000(1.15)^10/2 ≈21000(2.01)

So statement d is true.

If d is true, then so is e because d states that the tuition approximately doubles every 10 years.