Question

The total revenue from the sale of a popular book is approximated by the rational R(x) = 1000x^2/x^2 + 4, where x is the number of years since publication and the total revenue in millions of dollars. Use this function to complete parts a through d. (a) Find the total revenue at the end of the first year. $ million (b) Find the total revenue at the end of the second year. $ million (c) Find the domain of function R. Choose the correct domain below. x x x is a real number and x notequalto 2, x notequalto 5 x is a real number and x notequalto 2

Answer 1

a) 200 million dollars

b) 500 million dollars

c) Option A)

`\x`

Explanation:

We are given the following in the question:

`R(x) = (1000x^2)/(x^2 + 4)`

where R(x) is the revenue function in millions of dollars and x is the number of years since publication.

a) total revenue at the end of the first year

We put x = 1 in the revenue function

`R(1) = (1000(1)^2)/((1)^2 + 4) = 200`

Thus, the revenue after 1 year is 200 million dollars.

b) total revenue at the end of the second year

We put x = 2 in the revenue function

`R(2) = (1000(2)^2)/((2)^2 + 4) = 500`

Thus, the revenue after 2 year is 500 million dollars.

c) domain of function R

Domain:

It is the values of x for which the function R(x) is defined.

Since,

`x^2 + 4 \\eq 0, x \in R`

Thus, it is a proper function.

The domain is given by

Option A)

`\x`