Question

During the worst periods of hyperinflation in a certain country, the price of food increase at a rate of 10% per month. State whether this increases was linear or exponential. If your food bill was 100 in one month during this period, what was it three months later?

Answer 1

The increase was exponential

After three months his expense was: $133.1

Explanation:

The increase was exponential, because if we call x the initial price, then after the first month the new price p is:

`p = x (1 + (10\%)/(100\%))\\\\p=x(1+0.1)`

After the second month, the new price is 10% of the price of the previous month, that is:

`p = [x (1 + 0.1)](1 + 0.1)\\\\p = x (1 + 0.1) ^ 2`

After month n, the price is:

`p = x (1 + 0.1) ^ n`

Note that the equation has the form of an exponential growth function, where x is the initial price and n is the number of months elapsed.

In this case
`x = 100` and
`n = 3`. So:

`p = 100 (1 + 0.1) ^ 3\\\\p=\$133.1`