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The problem provided involves an exponential function modeling the future price of an item given an inflation rate of 2.8% per year. The function for the price, $ p(t) $, in terms of years from today $ t $, is:

\[
p(t) = 600(1.028)^t
\]

We are tasked with finding two things:
1. The current price of the item (which corresponds to $ t = 0 $).
2. The price of the item 9 years from today (which corresponds to $ t = 9 $).

### 1. Current price:
At $ t = 0 $:
\[
p(0) = 600(1.028)^0 = 600 \times 1 = 600
\]
Thus, the current price of the item is **$600**.

### 2. Price 9 years from today:
At $ t = 9 $:
\[
p(9) = 600(1.028)^9
\]
Now calculating this:
\[
p(9) \approx 600 \times (1.028)^9 \approx 600 \times 1.2682 = 760.92
\]
Rounding to the nearest dollar, the price 9 years from today is **$761**.

### Final Answers:
- Current price: **$600**
- Price 9 years from today: **$761**

Would you like further details on this calculation, or have any other questions?

Here are five related questions for further exploration:
1. How does increasing the inflation rate affect the future price?
2. What would the price be 5 years from today using the same model?
3. How would the model change if the inflation rate were 3% instead of 2.8%?
4. How does compound interest differ from simple interest in this context?
5. What is the mathematical meaning of exponential growth in financial terms?

**Tip:** To estimate future prices using inflation, understanding exponential growth is key because prices increase at an accelerating rate with time.

If the rate of inflation is 2.8% per year, the future price p(t) (in dollars) of a certain item can be modeled by the following exponential function, where t is the number of years from today: p(t) = 600(1.028)^t. Find the current price of the item and the price 9 years from today. Round your answers to the nearest dollar as necessary.

Learn how to calculate the future price of an item with a 2.8% inflation rate using the exponential growth formula p(t) = 600(1.028)^t. This problem involves finding the current price and the price 9 years from today, rounding to the nearest dollar. Ideal for students in Grades 9-12.

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