CPM Homework Help : CCA2 Problem 6-15

The cost of food has been increasing by $4\%$ per year for many years. To find the cost of an item $15$ years ago, Heather said, “Take the current price and divide it by $(1.04)^{15}$ .”

Her friend Elissa said, “No, you should take the current price and multiply it by $(0.96)^{15}$ !”

Explain who is correct and why.

Hint:

Since the situation describes an increase, the multiplier must be $1.04$ . In this situation, $x$ will represent cost.
What will $x$ be $15$ years in the past?

Answer:

Heather is correct, because a $4\%$ decrease does not ''undo'' a $4\%$ increase.