Question

1. quinn’s new motorcycle is valued at $15,000. with an annual depreciation rate of 25%, find the value of the motorcycle after 5 years. equation: ____________ value after 5 years: ____________

Explanation:

Step1: Identify the depreciation formula

The formula for exponential depreciation is \( V = P(1 - r)^t \), where \( V \) is the final value, \( P \) is the initial principal (value), \( r \) is the annual depreciation rate (as a decimal), and \( t \) is the time in years.
Here, \( P = 15000 \), \( r = 0.25 \) (since 25% = 0.25), and \( t = 5 \).

Step2: Substitute values into the formula

The equation is \( V = 15000(1 - 0.25)^5 \).

First, calculate \( 1 - 0.25 = 0.75 \). Then, calculate \( 0.75^5 \).
\( 0.75^5 = 0.75 \times 0.75 \times 0.75 \times 0.75 \times 0.75 \)
\( 0.75 \times 0.75 = 0.5625 \)
\( 0.5625 \times 0.75 = 0.421875 \)
\( 0.421875 \times 0.75 = 0.31640625 \)
\( 0.31640625 \times 0.75 = 0.2373046875 \)

Now, multiply by the initial value: \( V = 15000 \times 0.2373046875 \)
\( 15000 \times 0.2373046875 = 3559.5703125 \)

Answer:

Equation: \( V = 15000(1 - 0.25)^5 \)
Value after 5 years: \( \$3559.57 \) (or approximately \( \$3560 \) if rounded to the nearest dollar)