A new car is purchased for 22400 dollars. The value of the car depreciates at 11% per year. To the nearest tenth of a year , how long will it be until the value of the car is 5000 dollars?

t= 12.9 years

Step-by-step explanation:

Value after t years = initial value ( 1 - r )^t

Where,

Value after t years= $5000

Initial value = $22,400

r= depreciation rate = 11%

t= length of time (years)

Value after t years = initial value ( 1 - r )^t

5000 = 22,400 ( 1 - 0.11)^t

5000 = 22,400(0.89)^t

Divide both sides by 22,400

(0.89)^t = 5000 / 22,400

(0.89)^t = 0.2232

Take the log of both sides

t log 0.89 = log 0.2232

t= log 0.2232 / log 0.89

= -0.6513 / -0.0506

= 12.87

t= 12.9 years

77

step-by-step explanation: