Question

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation 2,000 = 16,000(1-r) t represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

Answer 1

Answer:

Step-by-step explanation:

Use the equation 2,000 = 16,000(1-r)^t to solve for t;

2000 = 16000(1-0.35)^t

Divide both sides by 16000

2000/16000 = 0.65^t

0.125 =0.65^t

Introduce logarithm on both sides;

ln 0.125 = t ln 0.65

Divide both sides by ln 0.65;

(ln 0.125) / (ln 0.65) = t

-2.07944/ -0.4308 = t

4.827 = t

t= 5 (as a whole number)

Therefore, the car is about 5 years old.