Questions: During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 15% per month. State whether this increase was linear or exponential. If your food bill was 120 in one month during this period, what was it three months later? Was the growth in inflation linear or exponential? - linear - exponential What was the monthly food bill after three months? (Round to the nearest dollar as needed.)

During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of 15% per month. State whether this increase was linear or exponential. If your food bill was 120 in one month during this period, what was it three months later? Was the growth in inflation linear or exponential? - linear - exponential What was the monthly food bill after three months? (Round to the nearest dollar as needed.)
Transcript text: During the worst periods of hyperinflation in a certain country, the price of food increased at a rate of $15 \%$ per month. State whether this increase was linear or exponential. If your food bill was $\$ 120$ in one month during this period, what was it three months later? Was the growth in inflation linear or exponential? linear exponential What was the monthly food bill after three months? \$ (Round to the nearest dollar as needed.)
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Solution

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Solution Steps

To determine whether the increase in the price of food is linear or exponential, we need to consider the nature of the percentage increase. A constant percentage increase per time period indicates exponential growth. To find the food bill after three months, we apply the formula for exponential growth, which is the initial amount multiplied by (1 plus the rate of increase) raised to the power of the number of periods.

Step 1: Determine the Nature of the Increase

The price of food increases at a rate of \( 15\% \) per month. Since this is a constant percentage increase, the growth is classified as exponential.

Step 2: Apply the Exponential Growth Formula

To find the food bill after three months, we use the exponential growth formula:

\[ B = P \times (1 + r)^t \]

where:

  • \( B \) is the final amount,
  • \( P = 120 \) is the initial food bill,
  • \( r = 0.15 \) is the monthly increase rate,
  • \( t = 3 \) is the number of months.

Substituting the values, we have:

\[ B = 120 \times (1 + 0.15)^3 \]

Step 3: Calculate the Final Food Bill

Calculating the expression:

\[ B = 120 \times (1.15)^3 \approx 120 \times 1.520875 = 182.505 \]

Rounding to the nearest dollar gives:

\[ B \approx 183 \]

Final Answer

The growth in inflation is exponential, and the monthly food bill after three months is \\(\boxed{183}\\).

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