Respuesta :
The car is about 6.6 years old.
Step-by-step explanation:
Given : An equation for the depreciation of a car is given by [tex]y = A(1-r)^t[/tex], 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. [tex]y=\frac{1}{2} A[/tex]
The rate of depreciation is 10% i.e. r=10%=0.1
Substitute in the equation, [tex]y = A(1-r)^t[/tex]
[tex]\frac{1}{2} A= A(1-0.1)^t[/tex]
[tex]\frac{1}{2}= (0.9)^t[/tex]
Taking log both side,
[tex]\log(\frac{1}{2})=t\log (0.9)[/tex]
[tex]t=\frac{\log(\frac{1}{2})}{\log (0.9)}[/tex]
[tex]t=6.57[/tex]
[tex]t\approx 6.6[/tex]
Therefore, the car is about 6.6 years old.
Answer:
The car is 6.5 years old
Step-by-step explanation:
An equation for the depreciation of a car is given by [tex]y = A(1 - r)^t[/tex]
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, [tex]y = \frac{A}{2}[/tex]
The rate of depreciation is 10% = 0.1 =r
Substitute the values in equation
[tex]\frac{A}{2} = A(1 - 0.1)^t[/tex]
[tex]\frac{1}{2} =(1 - 0.1)^t[/tex]
[tex]\frac{1}{2} =(0.9)^t[/tex]
[tex]0.5=0.9^t[/tex]
t=6.57
Hence The car is 6.5 years old