Question

An equation for the depreciation of a car is given by y = A(1-r)^twhere y = current value of the car, A = original cost, r = rate of
depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately
how old is the car?

Answer 1

Answer: The car is 6.6 years old.

Step-by-step explanation:

Hi, to answer this question we have to replace the values in the equation given:

Y = 1/2 (half the value)

A = 1 (total value)

r =10% = 0.10 (decimal form)

Replacing:

y = A(1-r)^t

1/2 = 1 (1-0.10)^t

Solving for t:

(1/2)/1 = 0.9^t

1/2 = 0.9^t

log 1/2 = log 0.9^t

log 1/2 = (t) log 0.9

(log 1/2)/ log 0.9 = t

6.57 =t

6.6 years (rounded)