Respuesta :

Answer:

The value C(t) of the car after  5  years is $12709.

Step-by-step explanation:

Given that Landon bought a new car for $16,000 and it depreciates 4.5% every year.

To find the value C(t) of the car after  5  years:

Initial value [tex]C(0)= $16,000[/tex]

Depreciation rate is  [tex]r=\frac{4.5}{100}[/tex]

∴ r=0.045

Period ,  t=5 years

[tex]C(t)=C(0)(1-r)^t[/tex]

Substitute the values we get

[tex]C(5)=16000(1-0.045)^5[/tex]

[tex]=16000(0.955)^5[/tex]

[tex]=16000(0.7943)[/tex]

∴ [tex]C(5)=12708.8[/tex]

The value C(t) of the car after  5  years is  $ 12709

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