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A new car is purchased for 22900 dollars. The value of the car depreciates at 6% per year. To the nearest year, how long will it be until the value of the car is 15700 dollars?

Respuesta :

Answer:6.1 years

Step-by-step explanation:

Given

Current worth [tex]C=\$ \ 22900[/tex]

rate of depreciates is [tex]D=6\ \%[/tex]  per year

worth after T years is [tex]W=\$ \ 15700[/tex]

Worth after T years

[tex]W=C(1-\frac{D}{100})^T[/tex]

[tex]15700=22900(1-\frac{D}{100})^T[/tex]

[tex]0.3776=0.94^T[/tex]

Taking log on  both sides

[tex]T=\dfrac{\ln 0.6855}{\ln 0.94}[/tex]

[tex]T=6.10\ years[/tex]

So it takes 6.1 years to  depreciate

Answer:

to the nearest year is 6

Step-by-step explanation:

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