Question

during the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 20% per month. state whether this increase was linear or exponential. if your food bill was \\$150 in one month during this period, what was it three months later?

was the growth in inflation linear or exponential?
linear
exponential

Explanation:

Identify the growth type

Using the Exponential Growth and Linear Growth knowledge points
The problem states that the price of food increases at a constant percentage rate of \(20\%\) per month. A constant percentage increase per unit of time represents exponential growth, whereas a constant absolute increase represents linear growth. Therefore, the growth is exponential.

Calculate the future value

Using the Exponential Growth knowledge point

$$ P_t = P_0 \times (1 + r)^t $$

Given:

• Initial food bill \(P_0 = \$150\)
• Monthly growth rate \(r = 20\% = 0.20\)
• Time period \(t = 3\) months

$$ P_3 = 150 \times (1 + 0.20)^3 $$

Compute the final amount

Using the Exponential Growth knowledge point

$$
LATEXBLOCK0
$$

The food bill three months later was \(\$259.20\).

Answer:

Question 1

• linear
• exponential (Correct answer)

Question 2

The food bill three months later was \(\$259.20\).