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.