Question

A college's tuition has risen 4% each year since 2000. If the tuition in 2000 was $9,850, write an equation for the amount of the tuition t years after 2000. Predict the cost of tuition for this college in 2025.

Answer 1

The required equation is

`y =9850(1.04)^t`

where y is the cost of tuition t years after 2000 in dollar.

The cost of tuition for this college in 2025 is $26258.49.

Explanation:

Given that, a college's tuition has risen 4% each since 2000.

The tuition fees in 2000 was $9,850.

The exponential growth formula:

`y=a(1+r)^t`

a= initial value

r= growth rate

t= time.

Here a= $9,850, r=4%=0.04

`\therefore y=9850(1+0.04)^t`

`\Rightarrow y =9850(1.04)^t`

The equation of the tuition is

`y =9850(1.04)^t`

where y is the cost of tuition in dollar.

In 2025, t= (2025-2000)=25 years.

Then the value of y when t=25 is

`y =9850(1.04)^(25)`

=$26258.49

The cost of tuition for this college in 2025 is $26258.49.