Exponential and Logarithmic Functions
Evaluating an exponential function that models a real-world situation

If the rate of inflation is $2.6 %$ per year, the future price $p (t)$ (in dollars) of a certain item can be modeled by the foll the number of years from today.
$p (t) = 2500 (1.026)^{t}$

Find the current price of the item and the price 10 years from today.
Round your answers to the nearest dollar as necessary.
Current price:
Price 10 years from today: $$ ◻$

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Answer

So, the price of the item 10 years from today will be approximately $6773, rounded to the nearest dollar. $6773$

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Step 1 ：The current price of the item is given by the function when t = 0. We know that any number raised to the power of 0 is 1, so: $p (0) = 2500 * (1.026)^{0} = 2500 * 1 = 2500$ . So, the current price of the item is $2500.

Step 2 ：To find the price 10 years from today, we substitute t = 10 into the function: $p (10) = 2500 * (1.026)^{10}$ .

Step 3 ：To calculate this, we first calculate the value of $(1.026)^{10}$ , and then multiply the result by 2500. $(1.026)^{10} \approx 2.709$ .

Step 4 ：So, $p (10) = 2500 * 2.709 \approx 6773$ .

Step 5 ：So, the price of the item 10 years from today will be approximately $6773, rounded to the nearest dollar. $6773$

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