Question

If the rate of inflation is per year, the future price (in dollars) of a certain item can be modeled by the following exponential function, where is the number of years from today: P=1200(1.019^)t Find the current price of the item and the price 10 years from today. Round your answers to the nearest dollar as necessary.

a) Current price: $1200; Price 10 years from today: $2194
b) Current price: $1200; Price 10 years from today: $1290
c) Current price: $1000; Price 10 years from today: $2194
d) Current price: $1000; Price 10 years from today: $1290

Answer 1

The current price of the item, according to the exponential function P=1200(1.019^t), is $1200. The price ten years from today is calculated by substituting 't' with 10, resulting in a price of approximately $1463.

Step-by-step explanation:

To calculate the future price of an item given the rate of inflation, we can use the provided exponential function P=1200(1.019t). The variable 't' represents the number of years from today, and the initial amount P is the current price of the item.

For the current price, we see that 't' would be 0 since we are looking for the price today. Therefore, P=1200(1.0190) which simplifies to P=1200 as any number raised to the power of 0 is 1.

To find the price 10 years from today, we substitute 't' with 10: P=1200(1.01910). Calculating this yields P=1200(1.219006171), which when rounded to the nearest dollar is approximately $1463. Hence, the correct current price of the item is $1200 and the price ten years from today is $1463.