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Grace [21]
3 years ago
6

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?
Mathematics
2 answers:
lesya692 [45]3 years ago
7 0

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

Mamont248 [21]3 years ago
3 0
<h2>The car is about 6.6 years old.</h2>

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.

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