The consumer price index for a given year is the amount of money in that year that has the same purchasing power as $100 in 1983. At the start of 2020 the CPi was 258.8. write a formula for the cpi as a function of t years after 2020, assuming that the CPI increases by 2.4% every year

To write a formula for the Consumer Price Index (CPI) as a function of $ t $ years after 2020, we start with the information provided:

- In 2020 (when $ t = 0 $), the CPI is 258.8.
- The CPI increases by 2.4% each year.

The formula for an exponentially growing quantity is:

\[
CPI(t) = CPI_0 \times (1 + r)^t
\]

Where:
- $ CPI_0 $ is the initial CPI (in this case, 258.8 in 2020),
- $ r $ is the growth rate (2.4%, or 0.024),
- $ t $ is the number of years after 2020.

Substituting the values:

\[
CPI(t) = 258.8 \times (1 + 0.024)^t
\]

\[
CPI(t) = 258.8 \times (1.024)^t
\]

This is the formula for the CPI as a function of $ t $, where $ t $ is the number of years after 2020.

### Do you want more details or have any questions?

Here are 5 related questions to think about:
1. What will the CPI be in 2025 using this formula?
2. How long will it take for the CPI to double?
3. What is the interpretation of a 2.4% increase in practical terms for consumers?
4. How does the CPI affect inflation calculations?
5. How would the formula change if the growth rate fluctuated each year?

**Tip:** Exponential growth is common in economic models because it reflects compound increases over time, making it important for long-term predictions.

The consumer price index for a given year is the amount of money in that year that has the same purchasing power as $100 in 1983. At the start of 2020 the CPI was 258.8. Write a formula for the CPI as a function of t years after 2020, assuming that the CPI increases by 2.4% every year.

Discover how to calculate the Consumer Price Index (CPI) as a function of time using the exponential growth formula. In this problem, the CPI starts at 258.8 in 2020 and increases by 2.4% each year. Learn how to apply the formula CPI(t) = 258.8 * (1.024)^t for accurate predictions, suitable for Grades 10-12.

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