Hi. Please help me with this?:

Suppose you start a home business typing technical research papers for college students. You must spend $3500 to replace your computer system. Then you estimate the cost of typing each page will be $.02. Write a rational function modeling your average cost per page.

If x is the number of pages typed, the total cost is 3500 + 0.02 x and the average cost per page is
3500/x + 0.02.

thanks!

You're welcome! That's correct. The rational function that models your average cost per page is:

Average cost per page = (Total cost) / (Number of pages) = (3500 + 0.02x) / x + 0.02

In this case, the total cost consists of the fixed cost ($3500) to replace your computer system plus the variable cost per page ($0.02x) multiplied by the number of pages typed (x). Then, to find the average cost per page, you divide the total cost by the number of pages.

You're welcome! I'm glad to help you with that.

To write a rational function modeling the average cost per page, you need to express the average cost per page as a function of the number of pages typed.

Given that the total cost is 3500 + 0.02x and the number of pages typed is x, the average cost per page can be calculated by dividing the total cost by the number of pages typed. So, the average cost per page is:

Average cost = (Total cost) / (Number of pages typed)
Average cost = (3500 + 0.02x) / x

Therefore, the rational function that models the average cost per page is:

f(x) = (3500 + 0.02x) / x

In this rational function, x represents the number of pages typed, and f(x) represents the average cost per page.

If you want to evaluate the average cost per page for a specific number of pages typed, you can substitute the value of x into the function. For example, if you typed 100 pages, you would substitute x = 100 into the function:

f(100) = (3500 + 0.02 * 100) / 100
f(100) = (3500 + 2) / 100
f(100) = 35.02 / 100
f(100) ≈ 0.3502

Therefore, the average cost per page for typing 100 pages would be approximately $0.3502.

I hope this explanation helps! Let me know if you have any further questions.

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