Question

77. The yearly cost of tuition (in-state) and required fees for

attending a public two-year college full time can be esti-

mated by the linear function f(x) = 64x + 2083, where x

is the number of years after 2000 and f(x) is the total cost.

(Source: The College Board)

a. Use this function to approximate the yearly cost of

attending a two-year college in the year 2016. (Hint: Find

f(16).]

b. Use the given function to predict in what year the yearly

cost of tuition and required fees will exceed $3200. [Hint:

Let f(x) = 3200, solve for x, then round your solution

up to the next whole year.]

c. Use this function to approximate the yearly cost of

attending a two-year college in the present year. If you

attend a two-year college, is this amount greater than or

less than the amount that is currently charged by the col-

lege you attend?

Answer 1

Answer:

a. $\ 3107$

b. 17 years

c. The amount that is currently charged by the college you attend is much higher than the amount charged in two-year college in the present year.

Step-by-step explanation:

a.

$f(x)=64x+2083$

Here, x is a the number of years after 2000 and f(x) is the total cost.

To approximate the yearly cost of  attending a two-year college in the year 2016,  find $f(16)$.

$f(16)=64(16)+2083\\\\=1024+2083\\\\=\ 3107$

b.

To predict in what year the yearly  cost of tuition and required fees will exceed $3200, solve $f(x)=3200$

$64x+2083=3200\\\\64x=3200-2083\\\\=1117\\x=\frac{1117}{64}\\\\ =17.45$

So,

x is approximately equal to 17 years.

c.

The present year is 2020.

To approximate the yearly cost of  attending a two-year college in the present year, find $f(20)$

$f(20)=64(20)+2083\\\\=1280+2083\\\\=\ 3363$

The amount that is currently charged by the college you attend is much higher than the amount charged in two-year college in the present year.