HOw to figure out purchase of car

Question

a car that when purchased 5 years ago coast $5000 has a value of $900. Find the value of the car of 8 years after its purchse by unig the exponential model V(t)=VoEtb, in which V(t) is the value of the car at any ltime t, Vo is the initial cost, t is the time in years and b is the rate of depreciation. Round to nearest hundredth

Answer 1

Using the 5 year depreciation data, we have:

 

V(5) = 5000*exp(5*b) = 900

 

taking the natural log of both sides after dividing both sides by 5000:

 

ln(900/5000) = 5b

 

b = -.343

 

So now V(8) = 5000*exp(8*-.343) = 5000*exp(-2.74) = $325.56