Question

Frank reads at least 24 pages but not more than 36 pages of a book. He reads 12 pages per hour.

The number of hours Frank reads p pages is modeled by a function.

t(p) = p12

What is the practical range of the function?

Answer 1

The real/true answer is all real numbers from 2 to 3, inclusive

(I took the test and it was correct)

Answer 2

Let

p-------> the number of pages

t-------> number of hours

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In this problem the unit rate is equal to the constant of proportionality k

`k=12(pages)/(hour)`

the linear equation is

`p=12t`

solve for t

`t(p)=p/12`

The domain of the function is the interval------->
`[24,36]`

because

`24\ pages \leq p \leq 36\ pages`

Find the range of the function

For
`p=24`

`t(24)=24/12=2\ hours`

For
`p=36`

`t(36)=36/12=3\ hours`

therefore

the answer is

The range of the function is the interval------->
`[2,3]`

because

`2\ hours \leq t \leq 3\ hours`