Question

1. Data from the American College Board show that in 2013, the average cost of tuition at private four- years colleges was $31,000. Since 2013, this number increased on average by about 3.7% each year.1) Let C denote the average cost of tuition at private four-year colleges, in dollars, and let t denotethe time in years since 2013. Write an exponential model that represents the average cost oftuition since the year 2013.2) if the trend continues, what is the average cost of tuition in 2020? Round decimal to two places.

Answer 1

Exponential growth formula

$f(t)=a(1+r)^t$

where:

• a: initial amount

,

• r: growth rate, as a decimal

,

• t: time

1) In this case, the function is denoted by variable C(t), t indicates the time in years since 2013, the initial amount is a = 31,000, and the growth rate is r = 0.037 (= 3.7/100). Substituting these values into the formula, we get:

$\begin{gathered} C(t)=31000(1+0.037)^t \\ C(t)=31000(1.037)^t \end{gathered}$

2) In 2020, 7 years have passed since 2013, then t = 7. Substituting into the formula:

$\begin{gathered} C(t)=31000(1.037)^7 \\ C(t)=39977.26 \end{gathered}$