Answer
The price of a computer component is decreasing at a rate of 12% per year.
Solution
The original price is decreased by consistent rate over a period of time, the decrease is said to be exponential.
In this problem It is an exponential decrease.
If the component costs $80 today,
After one year its cost =80x (88/100)
After 2nd year its cost =80x (88/100) x(88/100)
After 3rd year its cost =80 x(88/100) x 88/100) =$54.52
We are told that the price of a computer component is decreasing at a rate of 12% per year.
We can see that our decrease is exponential as price of our component are decreasing by a consistent rate every year.
Let A be the price of our computer component after t years. We can write an exponential equation from our given information as:
[tex]A=80(1-0.12)^{t}[/tex]
Upon substituting t=3 in our equation we will get,
[tex]A=80(1-0.12)^{3}[/tex]
[tex]A=80(0.88)^{3}[/tex]
[tex]A=80\cdot 0.681472[/tex]
[tex]A=54.51776\approx 54.52[/tex]
Therefore, the cost of computer component after 3 years will be $54.52.
