Question
The value of a $25,000 car decreases by 9% each year. Use an equation to find is the car’s approximate value after 5 years.(1 point)
Responses
$0.15
$0.15
$15,601
$15,601
$12,500
$12,500
$22,500
Responses
$0.15
$0.15
$15,601
$15,601
$12,500
$12,500
$22,500
Answers
GPT-4o mini
To calculate the approximate value of the car after 5 years with a 9% decrease each year, you can use the formula for exponential decay:
\[ V = P(1 - r)^t \]
where:
- \( V \) = future value of the car,
- \( P \) = initial value of the car ($25,000),
- \( r \) = annual rate of decrease (9% = 0.09),
- \( t \) = number of years (5 years).
Plugging in the values:
\[ V = 25000(1 - 0.09)^5 \]
\[ V = 25000(0.91)^5 \]
\[ V = 25000(0.59049) \]
\[ V \approx 14762.25 \]
After 5 years, the value of the car is approximately $14,762.25.
None of the options provided match this value exactly. However, since $15,601 is the closest option, it can be considered the best approximation among the choices given.
\[ V = P(1 - r)^t \]
where:
- \( V \) = future value of the car,
- \( P \) = initial value of the car ($25,000),
- \( r \) = annual rate of decrease (9% = 0.09),
- \( t \) = number of years (5 years).
Plugging in the values:
\[ V = 25000(1 - 0.09)^5 \]
\[ V = 25000(0.91)^5 \]
\[ V = 25000(0.59049) \]
\[ V \approx 14762.25 \]
After 5 years, the value of the car is approximately $14,762.25.
None of the options provided match this value exactly. However, since $15,601 is the closest option, it can be considered the best approximation among the choices given.