Chapter 5, Problem 57RE

Rising Tuition The following data represent the average in-state tuition and fees (in 2013 dollars) at public four- year colleges and universities in the United States from the academic year 1983 84 to the academic year 2013 14.

(a) Using a graphing utility, draw a scatter diagram with academic year as the independent variable.

(b) Using a graphing utility, build an exponential model from the data.

(c) Express the function found in part (b) in the form $A\left(t\right)\text{ = }{A}_0{e}^{kt}$.

(d) Graph the exponential function found in part (b) or (c) on the scatter diagram.

(e) Predict the academic year when the average tuition will reach $\$12,000$.

To determine

To find:

a. Using a graphing utility, draw a scatter diagram with academic year as the independent variable.

Answer to Problem 57RE

a.

Explanation of Solution

Given:

Exponential model.

Calculation:

a. Graph:

To determine

To find:

b. Using a graphing utility, build an exponential model from the data.

Answer to Problem 57RE

b. $y=2638.26{\left(1.047\right)}^x$

Explanation of Solution

Given:

Exponential model.

Calculation:

b. $y=2638.26{\left(1.047\right)}^x$

To determine

To find:

c. Express the function found in part (b) in the form $A=A_0{e}^{kt}$.

Answer to Problem 57RE

c. $y=2638.26e^{0.0399x}$

Explanation of Solution

Given:

Exponential model.

Calculation:

c. $y=2638.26e^{0.0399x}$

To determine

To find:

d. Graph the exponential function found in part(b) or (c) on the scatter diagram.

Answer to Problem 57RE

d.

Explanation of Solution

Given:

Exponential model.

Calculation:

d.

To determine

To find:

e. Predict the academic year when the average tuition will reach $\$12000$.

Answer to Problem 57RE

e. 2021-22

Explanation of Solution

Given:

Exponential model.

Calculation:

e. $y=2638.26e^{0.0399x}$

$12000=2638.26e^{0.0399x}$

$1.514=e^{0.0399x}$

$x\approx 38$

Therefore 2021-22.