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A motorcycle is depreciating at 15% per year, every year. A student's $15,200 motorcycle
depreciating at this rate can be modeled by the equation V(t) = 15,200(0.85). What is an equivalent
equation for this vehicle as a monthly depreciation and, using this equation, what is the motorcycle
worth (rounded to the nearest hundred dollar) 7 years after purchase?
Ov(t) = 15,200(0.8700)12, $13,800
Ov(t) = 15,200(0.9865), $4,900
Ov(t) = 15,200(1.15)-# $5,700
Ov(t) = 15,200(0.9865)12t, $4,900

Respuesta :

MrRoyal

The monthly depreciation is [tex]V(t) = 15200(0.9865)^t[/tex], and the value after 7 years is (d) $4900

The yearly depreciation is given as:

[tex]V(t) = 15200(0.85)^t[/tex]

There are 12 months in a year, so the monthly depreciation would be

[tex]V(t) = 15200(0.85)^{\frac{t}{12}}[/tex]

Where t represents the number of months

Rewrite the expression as:

[tex]V(t) = 15200(0.85^\frac{1}{12})^t[/tex]

Evaluate the exponent of 1/12

[tex]V(t) = 15200(0.9865)^t[/tex]

After 7 years, we have:

[tex]t =7 \times 12[/tex]

[tex]t =84[/tex]

So, the value of the motorcycle after 7 years is

[tex]V(84) = 15200(0.9865)^{84}[/tex]

[tex]V(84) = 4852.88[/tex]

Approximate to the nearest hundred dollar

[tex]V(84) = 4900[/tex]

Hence, the value after 7 years is (d) $4900

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