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kakasveta [241]
3 years ago
7

A motorcycle is depreciating at 12% per year, every year. A student's $11,250 motorcycle depreciating at this rate can be modele

d by the equation V(t) = 11,250(0.88)t. 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) 8 years after purchase?
Mathematics
1 answer:
Aleksandr [31]3 years ago
5 0
For this case we have an equation of the form:
 y = A (b) ^ t

 Where,
 A: initial amount
 b: decrease rate
 t: time
 In this case we have the following equation:
 V (t) = 11,250 (0.88) ^ t

 Where,
 t: number of years
 Rewriting for the number of months we have:
 V (t) = 11,250 (0.88) ^ {((1/12) * t)}

 Where,
 t: number of months
 For 8 years (96 months) we have:
 V (96) = 11.250 (0.88) ^ {((1/12) * 96)}

V (96) = 4045.888404
 round to the nearest hundred dollar:
 V (96) = $ 4050
 Answer:
 
V (t) = 11,250 (0.88) ^ {((1/12) * t)}

V (96) = $ 4050
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