Question

He price of a computer component at the QRCC bookstore is decreasing at a rate of 2.25% per year. Decide whether this decrease is linear or exponential.

Answer 1

The decrease is exponential.

Explanation:

An exponential decrease is something like:

f(x) = A*(r)^x with 0 < r < 1

A linear decrease is something like:

g(x) = -a*x + b with a > 0

First ai general formula.

If you have a quantity Q, decreased by an X%, the new quantity will be:

New Quantity = Q - Q*(X%/100%)

Now let's look at the question:

Suppose that the original price of the computer component is K

And the price as a function of the year is P(y)

Then we know that, in the year zero, the price is K.

P(0) = K

One year after, the price decreases by 2.25%

Then:

P(1) = K - K*(2.25%/100%) = K*(1 - 0.0225)

After another year, we will have another decrease of 2.25%

Then:

P(2) = K*(1 - 0.0225) - K*(1 - 0.0225)*(2.25%/100%)

P(2) = K*(1 - 0.0225)*(1 - 0.0225) = K*(1 - 0.0225)^2

We already can see the pattern, we can expect that in the year y, the price of the component will be:

P(y) = K*(1 - 0.0225)^y

This clearly is an exponential decrease.