Question

The annual tuition at a specific college was $20,500 in 2000, and $454,120 in 2018. Let x be the year since 2000, and y be the tuition. Write an equation that can be used to find the tuition y for x years after 2000. Use your equation to estimate the tuition at this college in 2020. In the form of y =mx+b.

Answer 1

The equation that can be used to find the tuition y for x years after 2000 is:

`y=24090x-3590`

The tuition in 2020 is estimated to be $478,210

Step-by-step explanation:

In 2000, the tuition was $20,500

In 2018, the tuition was $454,120

SInce x is the year since 2000, and y is the tuition, we want to write an equation that can be used to find the tuition y for x years after 2000

The equation is linear, as indicated at the end of the question: y = mx + b

The first term is 20500 in 2000

The last term (19th term) is 454120 in 2018

We have the nth term of a sequence to be:

`T_n=a+(n-1)d`

where a is the first term, and d is the common difference.

We need to know the common difference

`\begin{gathered} 454120=20500+(19-1)d \\ \\ 454120-20500=18d \\ \\ 433620=18d \\ \\ d=(433620)/(18)=24090 \end{gathered}`

Knowing the common difference, we now have the equation:

`y=24090(x-1)+20500`

OR

`y=24090x-3590`

This is in the form :

`\begin{gathered} y=mx+b \\ \\ \text{where m = 24090, and b = -3590} \end{gathered}`

Now, to estimate the tuition at this college in 2020, because this is 20 years after year 2000, we have x = 20

Using this in the last equation, we have:

`\begin{gathered} y=24090(20)-3590 \\ \\ =481800-3590 \\ \\ =478210 \end{gathered}`

The tuition in 2020 is estimated to be $478,210