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:The increase was exponentialAfter three months his expense was: $133.1Step-by-step explanation:The increase was exponential, because if we call x the initial price, then after the first month the new price p is:[tex]p = x (1 + \frac{10\%}{100\%})\\\\p=x(1+0.1)[/tex]After the second month, the new price is 10% of the price of the previous month, that is:[tex]p = [x (1 + 0.1)](1 + 0.1)\\\\p = x (1 + 0.1) ^ 2[/tex]After month n, the price is:[tex]p = x (1 + 0.1) ^ n[/tex]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 [tex]x = 100[/tex] and [tex]n = 3[/tex]. So:[tex]p = 100 (1 + 0.1) ^ 3\\\\p=\$133.1[/tex]