Question

6. The equation ft) = 13,000(1.024)^t models the annual tuition at a private school over time, t. By what percent does the tuition increase each year? a. 0.24% b. 2.4% C. 1.024% d. 24%

Answer 1

We have the expression:

`f(t)=13000\cdot(1.024)^t`

We can find how much the annual tuition increases each year by calculating:

`\begin{gathered} \Delta=(f(t+1)-f(t))/(f(t))=(f(t+1))/(f(t))-1=(13000\cdot(1.024)^(t+1))/(13000\cdot(1.024)^t)-1 \\ \Delta=1.024^{\mleft\{t+1-t\mright\}}-1=1.024-1=0.024\cdot100\%=2.4\% \end{gathered}`

Answer: b. 2.4%