Question

question 1-14
bridget purchases a new car for $40,000. new cars lose approximately 2% of their value each month for the first several months of ownership.
select the equation below that bridget could use to estimate the value of her car after 3 years of ownership.
\\( v = 40,000 - 0.02t \\)
\\( v = 40,000(0.98)^t \\)
\\( v = 40,000(1.02)^t \\)
\\( v = 40,000 + 0.98t \\)

Explanation:

Step1: Identify decay type

This is exponential decay, since the car loses a percentage of its value each month, not a fixed dollar amount.

Step2: Calculate remaining value factor

If the car loses 2% monthly, it retains \(100\% - 2\% = 98\% = 0.98\) of its value each month.

Step3: Match to exponential decay formula

The general exponential decay formula is \(V = P(1-r)^t\), where \(P=40000\), \(r=0.02\), so \(V = 40000(0.98)^t\).

Answer:

$\boldsymbol{V = 40,000(0.98)^t}$