Algebra 2 question

Question

You pay $300 for canning supplies plus $0.40 for each food item you can.

a. How many canned items must you complete for the average cost per canned item to fall to $1?

canned items

b. What happens to the average cost as you complete more canned items?

As the number of canned items increases, the average cost approaches $

Answer 1

a)

The average cost per can is equal to the amount you pay over the number of cans.

Average = Amount paid / number of cans

Let n be the number of cans. The amount paid in dollars would therefore be 300 + 0.40n

So,

Average = (300 + 0.40n) / n

Set the average equal to 1 and solve for n

You should get n = 500 cans

b)

This requires a limit. You want to know what happens to the average as n becomes really high.

lim (300 + 0.40n) / n

^n→∞

The $300 becomes more and more insignificant with every can you buy.

Therefore, you can reduce the limit to:

lim (0.40n) / n = 0.40

^n→∞

Therefore, the average cost approaches $0.40