Question

The price of a computer component is decreasing at a rate of 12% per year. State whether this decrease is linear or exponential. If the component costs $80 today, what is the cost in 3 years?

Answer 1

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:

`A=80(1-0.12)^(t)`

Upon substituting t=3 in our equation we will get,

`A=80(1-0.12)^(3)`

`A=80(0.88)^(3)`

`A=80\cdot 0.681472`

`A=54.51776\approx 54.52`

Therefore, the cost of computer component after 3 years will be $54.52.

Answer 2

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