Question

A new car is purchased for $41,000 and over time its value depreciates by one halfevery 3 years. What is the value of the car 4 years after it was purchased, to thenearest hundred dollars?

Answer 1

approxLet's do it step by step

We know that the value of the car depreciates every three years, this can be interpreted as if its value is decreasing by 1/6 every year. Why do we do this? Because we need a 'softer' function that simply saying that suddenly the car lost has of its value after three years.

So, after the first year:

The car loses 1/6 of its original value, so, after the first year, its value is 5/6(41000)=34167 aprox.

We repeat this procedure for the remaining four years, and notice that it's like if the original value of the car was multiplied by 5/6 four times in total!

For example: after the second year the car's value is:

5/6*5/6*41000

So, after the fourth year: the value of the car is: (5/6)^4 * 41000=19772 and to the nearest hundred dollars: 19800