Solved on Dec 04, 2023
The price of a computer component decreases by per year. Is the decline linear or exponential? If the component costs today, what will it cost in three years?
Is the decline in price linear or exponential?
exponential
What will the component cost in three years?
STEP 1
Assumptions
1. The price of the computer component is decreasing at a rate of 13% per year.
2. The current cost of the component is $50.
3. We want to find the cost of the component in three years.
4. The decrease in price is compounded annually.
STEP 2
First, we need to determine whether the decrease in price is linear or exponential. In a linear decrease, the price would decrease by a fixed amount each year. In an exponential decrease, the price decreases by a fixed percentage each year. Since the problem states that the price is decreasing by a fixed percentage (13%) each year, this is an exponential decrease.
STEP 3
Now, we need to calculate the cost of the component in three years. We can do this using the formula for exponential decay, which is:
where:
- is the final price,
- is the initial price,
- is the rate of decrease (expressed as a decimal), and
- is the time in years.
STEP 4
Plug in the given values for the initial price, rate of decrease, and time to calculate the final price.
STEP 5
Calculate the final price.
The component will cost approximately $32.93 in three years.
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