Question

an equation for the depreciation of a car is given by (y = a(1 - r)^t), where (y =) current value of the car, (a =) original cost, (r =) rate of depreciation, and (t =) time, in years. the current value of a car is $12,282.50. the car originally cost $20,000 and depreciates at a rate of 15% per year. how old is the car?

(\frac{1}{4}) years

(\frac{1}{3}) years

3 years

4 years

Explanation:

Identify given values and formula

Using the Exponential Decay Modeling knowledge point

$$
LATEXBLOCK0
$$

Substitute values into the equation

Using the Exponential Decay Modeling knowledge point

$$
LATEXBLOCK1
$$

Isolate the exponential term

Using the Algebraic Simplification knowledge point

$$
LATEXBLOCK2
$$

Solve for the exponent t

Using the Solving Exponential Equations Algebraically knowledge point

$$
LATEXBLOCK3
$$

Answer:

• (A) \(\frac{1}{4}\) years
• (B) \(\frac{1}{3}\) years
• (C) 3 years (Correct answer)
• (D) 4 years