Sam bought a new car for $26,500. The car depreciates approximately 13% of its value each year.
a) What is the decay factor for the value of this car?
b) Write an equation to model the decay value of this car?
c) What will the value of the car be in 10 years?
Assume that the value of the car decreases exponentially: V = V_0 * e^(-a *t), where a is the decay factor and t is the time in years. After the first year t = 1, V = 0.87 V_0 and e^(-a) = 0.87.
a) the decay factor is a = - ln(0.87) = 0.139
b) the equation is V = 26500*e^(-0.139*t)
c) in 10 years the value of the car will be 26500*e^(-1.39) = $6600.
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