The price of a computer component is decreasing at a rate of 13% per year. State whether this decrease is linear or exponential. If the component costs $110 today, what
will it cost in three years?
The decrease in price of the computer component is exponential because it is decreasing at a constant percentage rate each year.
To find the price of the computer component in three years, we need to use exponential decay. We can use the formula:
P = P0(1 - r)^t
Where:
P = final price
P0 = initial price
r = rate of decrease as a decimal
t = time in years
Given:
P0 = $110
r = 13% = 0.13
t = 3 years
Plugging in the values into the formula, we have:
P = 110(1 - 0.13)^3
P = 110(0.87)^3
P ≈ 110(0.658)
Therefore, the computer component will cost approximately $72.38 in three years.