Question

An equation for the depreciation of a car is given by y = A(1 – r)t , where 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 6.5 years old

Step-by-step explanation:

An equation for the depreciation of a car is given by $y = A(1 - r)^t$

y = current value of the car

A = original cost

r = rate of depreciation

t = time in years

The value of a car is half what it originally cost

So, $y = \frac{A}{2}$

The rate of depreciation is 10% = 0.1 =r

Substitute the values in equation

$\frac{A}{2} = A(1 - 0.1)^t$

$\frac{1}{2} =(1 - 0.1)^t$

$\frac{1}{2} =(0.9)^t$

$0.5=0.9^t$

t=6.57

Hence The car is 6.5 years old

Answer 2

The car is about 6.6 years old.

Step-by-step explanation:

Given : An equation for the depreciation of a car is given by $y = A(1-r)^t$, where 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%.

To find : Approximately how old is the car?

Solution :

The value of a car is half what it originally cost i.e. $y=\frac{1}{2} A$

The rate of depreciation is 10% i.e. r=10%=0.1

Substitute in the equation, $y = A(1-r)^t$

$\frac{1}{2} A= A(1-0.1)^t$

$\frac{1}{2}= (0.9)^t$

Taking log both side,

$\log(\frac{1}{2})=t\log (0.9)$

$t=\frac{\log(\frac{1}{2})}{\log (0.9)}$

$t=6.57$

$t\approx 6.6$

Therefore, the car is about 6.6 years old.