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.
Accepted Solution
A:
Answer:Step-by-step explanation:Use the equation 2,000 = 16,000(1-r)^t to solve for t;2000 = 16000(1-0.35)^tDivide both sides by 160002000/16000 = 0.65^t0.125 =0.65^tIntroduce logarithm on both sides;ln 0.125 = t ln 0.65Divide both sides by ln 0.65;(ln 0.125) / (ln 0.65) = t-2.07944/ -0.4308 = t4.827 = tt= 5 (as a whole number)Therefore, the car is about 5 years old.