Question

7. Use this information for the following questions. In 2019, the cost of tuition at a community college was $384per credit hour. The school plans the cost of tuition to rise up to $442 per credit hour in 2022. Round to twodecimal places for all parts of this problem.a. Find the rate of change of the cost of tuition during this time span, write answer as a decimalb. Write a formula for the cost of tuition as a function of the number of years since 2019,c. What will the tuition be in 2025?d. What year will the tuition be $500 per credit hour?

Answer 1

Let:

$\begin{gathered} (x1,y1)=(2019,384) \\ (x2,y2)=(2022,442) \end{gathered}$

a. The rate of change (the slope) is given by:

$m=\frac{y2-y1}{x2-x1}=\frac{442-384}{2022-2019}=\frac{58}{3}\approx19.33$

b.

Using the point-slope equation:

$\begin{gathered} y-y1=m(x-x1) \\ y-384=\frac{58}{3}(x-2019) \\ y-384=\frac{58}{3}x-39034 \\ y(x)=\frac{58}{3}x-38650 \end{gathered}$

c.

$\begin{gathered} x=2025 \\ y(2025)=\frac{58}{3}(2025)-38650 \\ y(2025)=39150-38650 \\ y(2025)=500 \end{gathered}$

d.

$\begin{gathered} 500=\frac{58}{3}x-38650 \\ \frac{58}{3}x=500+38650 \\ \frac{58}{3}x=39150 \\ x=2025 \end{gathered}$

In the year 2025