Question

the price of a computer component is decreasing at a rate of 9% per year. state whether this decrease is linear or exponential. if the component costs $60 today, what will it cost in three years?

is the decline in price linear or exponential?

• exponential
• linear

Explanation:

Identify the type of decrease

$$ \text{Rate of decrease} = 9\% \text{ per year} $$

Since the decrease is a constant percentage of the value each year rather than a constant absolute amount, the decline is exponential.

Formulate the exponential decay model

$$ P(t) = P_0 (1 - r)^t $$

$$ P(t) = 60 (1 - 0.09)^t = 60 (0.91)^t $$

Calculate the price after three years

$$ P(3) = 60 (0.91)^3 = 60 (0.753571) = 45.21426 $$

$$ P(3) \approx \$45.21 $$

Answer:

• exponential (Correct answer)
• linear