The initial value of a car is $30,000. After one year, the value of the car is $20,000. Estimate the value of the car after five years.

Question

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Answer 1

The formula for exponential decay is y = a*b^t where y is the current value, a is the initial value, b is the base (which equals 1 minus the decay rate), and t is time.  

 

You can use the given information to figure out what b is.  

 

20000 = 30000*b¹

b = 2/3

 

Now that you know what b is, you can plug in 5 for t to figure out the value after five years.   

 

y = 30000*(2/3)⁵ = 3950.62  

 

So the estimated value after 5 years is $3950.62