A new car is purchased for 15600 dollars. The value of the car depreciates at 12.25%

per year. To the nearest tenth of a year, how long will it be until the value of the car is

2700 dollars?

13.4 years exponential depreciation, because a car no matter how old should have some value. If I chose a linear depreciation, then it is possible for the car to have negative value, which is not realistic.

Step-by-step explanation:

Your starting value is $15,600

Use the formula V = P * (1 - r*t)

Assuming the depreciation is linear instead of exponential.

$2,700 = $15,600 * (1 - 0.1225*t)

solve for t.

2700/15600 = 1 - 0.1225*t

27/156 = 1 - 0.1225*t

0.1225 * t = 1 - 27/156

t = (1/0.1225) * (1 - 27/156)

t = (1/0.1225) * (129/156)

t = 6.7503924 years

Assuming an exponential depreciation:

V = P * (1 - r) ^t

$2,700 = $15,600 * (1 - 0.1225) ^t

$2,700 = $15,600 * (0.8775) ^t

2700/15600 = 0.8775^t

27/156 = 0.8775^t

ln (27/156) = ln (0.8775^t)

ln (27/156) = t * ln (0.8775)

-1.754019141 = t * - 0.1306783236

t = - 1.754019 / - 0.130678323 = 13.42 years ... if this was exponential depreciation.

Answer: A new car is purchased for 15600 dollars. The value of the car depreciates at 12.25%

per year. To the nearest tenth of a year, how long will it be until the value of the car is

2700 dollars