Chapter 9.9, Problem 52HP

To determine

To describe an example of real world situation in which write two functions $f(x)$and $g(x)$ , and substract $(f-g)(x)$ , and .

Answer to Problem 52HP

  $f(x)$is revenue

  $f(x)=-0.01x2+3.5x,$

  $g(x)$is cost

  $g(x)=0.00007x3-0.01x2+1.26x+84$

Profit $=(f-g)(x)$

  $(f-g)(x)=0.00007x3+3.24x-84$

Explanation of Solution

Given information:

Example of real world

Functions are $f(x)$and $g(x)$

Find $(f-g)(x)$

Suppose M is the CEO of a successful company, and M is presenting the accounting records for the past year at a meeting.M explain that company's revenue, or the money coming in, can be modeled using the following formula:

  $f(x)=-0.01x2+3.5x,$

where x is the number of products produced and sold by the company,

and f is in thousands of dollars.

M also display a formula that can model company's cost, or the amount of money going out.

  $g(x)=0.00007x3-0.01x2+1.26x+84$

where x is the number of products produced and sold by the company, and g is in thousands of dollars.

In mathematics, these formulas real-valued functions.

If employees at the meeting ask if M could find a formula for how much money company is actually making.In other words, employees want to find a formula for company's profit. Let's see… revenue equals money in, and cost equals money out.

If subtract the cost from the revenue, will have profit.

A formula for revenue, $f(x)$ , and for cost, $g(x)$

Therefore, a formula for profit by subtracting $g(x)$ from f(x).

  $\mathrm{Pr}ofit=(f-g)(x)$

Substituting value of , $f(x)$and $g(x)$

  $(f-g)(x)=-0.01x2+3.5x-(0.00007x3-0.01x2+1.26x+84)$

On solving,

  $(f-g)(x)=0.00007x3+3.24x-84$