Question

During the worst periods of inflation in America, the price of food increased at a rate of 12 % per month. If your food bill was $300 one month during this period, what was it two months later?

Exponential; $337.08
Linear; $672.00
Exponential; $376.32
Linear; $372.00

Answer 1

Exponential; $376.32

Explanation:

Generally, an increase of 12% in a month means the prices are 12% more than they were in the previous month. That is, the value has been multiplied by 1.12.

The same would be true for the second month, so the overall multiplier for the two months is ...

(1.12)(1.12) = 1.12^2 = 1.2544

This makes the food bill for the second month amount to ...

1.2544 × $300 = $376.32

_____

As with all percentages, you need to be clear about what base is being used. Here, we have assumed the base for a monthly increase is the value at the beginning of the month.

If, instead, it is the value at the beginning of the year, then the increase is linear, not exponential. 12% of the value at the beginning of the year is the same throughout the year.