Chapter 7.7, Problem 4GP

To determine

Write an equation for the amount of tuition t years after 2010 and to predict the cost of tuition for the college in year 2025.

Answer to Problem 4GP

The equation for the amount of tuition t years after 2010 is $y=10850\cdot {\left(1.05\right)}^t$ .

The cost of tuition for this college in year 2025 is $22556.

Explanation of Solution

Given information:

Initial cost of tuition in 2010 is $10,850.

Growth rate of tuition is 5% each year.

Calculation:

We know the exponential function equation is $y=a\cdot b^t$ , where $a\text{ is intial cost of tuition,}$

  $b\text{ is the growth factor,}$ and t is the number of years after 2010.

Also $b=1+r$ where r is growth rate.

We got,

Initial value $(a)$ = $10,850 and

Growth factor $(b)$ =1+0.05=1.05.

Plugging the value of a and b in exponential function equation

  $y=a\cdot b^x$

  $y=10850\cdot {\left(1.05\right)}^t$ , where t is years after 2010. ---------- (I)

Therefore, the equation for the amount of tuition t years after 2010 is

  $y=10850\cdot {\left(1.05\right)}^t$ .

For year 2025 the value of t is

  $=2025-2010=15years.$

Now, plugging the value t =15 in equation

  $y=10850\cdot {\left(1.05\right)}^t.$

  $y=10850\cdot {\left(1.05\right)}^{15}$

  $y\approx 22556.37$

Therefore, the cost of tuition for this college in year 2025 is approximately $22556.