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.

here is my work $19,400. = $12,105.(1-r)^3
$12,105. = $12,105.
=9.105 = 1-r
=3.01
=x
please help me

Answer 1

19400(1-r)^3 = 12105

That is, the starting value declines each year
So, not only is your first step backwards, the rest of your steps are just nonsense
Next, divide by 19400 to get
(1-r)^3 = 12105/19400 = 0.62396
now take the cube root:
1-r = 0.85452
r = 0.15
so, the value declines by 15% each year

Answer 2

ok thank's sir or miss

Answer 3

To find the rate of decline in the value of the car, you can use the formula:

Current Value = Initial Value * (1 - Rate of Decline)^Time

Substituting the given values into the formula:

$12,105 = $19,400 * (1 - Rate of Decline)^3

To isolate the rate of decline, we can rearrange the equation:

(1 - Rate of Decline)^3 = $12,105 / $19,400

Taking the cube root of both sides:

1 - Rate of Decline = ( $12,105 / $19,400 )^(1/3)

Subtracting 1 from both sides:

Rate of Decline = 1 - ( $12,105 / $19,400 )^(1/3)

Calculating the expression within the parentheses:

Rate of Decline = 1 - (0.625)^(1/3)

Now, we can compute the value:

Rate of Decline ≈ 1 - 0.871 = 0.1291

So, the rate of decline in the value of the car is approximately 12.91%.

Answer 4

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

Final Value = Initial Value * (1 - Rate of Decline)^Number of Years

In this case, the initial value of the car is $19,400, the final value is $12,105, and the number of years is 3. Let's plug in these values into the formula:

$12,105 = $19,400 * (1 - Rate of Decline)^3

Next, divide both sides of the equation by $19,400:

$12,105 / $19,400 = (1 - Rate of Decline)^3

Simplify the left side of the equation:

0.625 = (1 - Rate of Decline)^3

Now, we need to find the cube root of both sides of the equation to isolate the (1 - Rate of Decline):

∛0.625 = 1 - Rate of Decline

The cube root of 0.625 is approximately 0.857, so:

0.857 ≈ 1 - Rate of Decline

To find the Rate of Decline, subtract 0.857 from 1:

Rate of Decline = 1 - 0.857

Rate of Decline ≈ 0.143

Therefore, the rate of decline in the value of the car is approximately 0.143, or 14.3%.