A new car is sold for its sticker value of $19,400. Three years later, the customer returns to the car dealership to trade the car in. She is told that her car now has a value of $12,105. What is the rate of decline in the value of the car? In your final answer, include all of your calculations.

Question

A new car is sold for its sticker value of $19,400. Three years later, the customer returns to the car dealership to trade the car in. She is told that her car now has a value of $12,105. What is the rate of decline in the value of the car? In your final answer, include all of your calculations.

Answer 1

19400(1-r)^3 = 12105

(1-r)^3 = .623969..
take cube root of both sides, etc

Answer 2

To find the rate of decline in the value of the car, we need to calculate the difference in value over the three-year period and then determine the rate of that decline.

Step 1: Calculate the difference in value:
Value decline = Sticker value - Current value
= $19,400 - $12,105
= $7,295

Step 2: Calculate the rate of decline:
Rate of decline = Value decline / Sticker value
= $7,295 / $19,400
≈ 0.376

Step 3: Convert the rate to a percentage:
Rate of decline (as a percentage) = Rate of decline x 100
≈ 0.376 x 100
≈ 37.6%

The rate of decline in the value of the car over the three-year period is approximately 37.6%.

Answer 3

To find the rate of decline in the value of the car, we can use the formula for calculating the rate of change:

Rate of change = (Final Value - Initial Value) / Time

Here, the initial value is the sticker value of $19,400, the final value is $12,105, and the time is 3 years.

Let's plug these values into the formula:

Rate of decline = ($12,105 - $19,400) / 3

= -$7,295 / 3

= -$2,431.67

So, the rate of decline in the value of the car is approximately -$2,431.67 per year.

Note: The negative sign indicates a decline in value, and the rate is rounded to two decimal places.