Question

The value of a car declines 20% per year. What percent of the original value remains after 2 year?

Answer 1

So we can express this as a function of time. \[f(t)=V _{i}-\frac{ 20V _{i} }{ 100 year } t=Vi(1-\frac{ 0.2 }{ year } t)\]Where "Vi" is the initial value and "t" is the number of years. I got that equation by saying: "Well the value must be a function of time in the following way. Since it is always the original value minus 20% of that original value each year, the equation must be:" If we replace t for 2 years we get :\[f(2year)=V _{i}(1-\frac{ 0.2 }{ year }2year)=0.6V _{i}\]That mean that the car is worth 60% of its original value.

Answer 2

This is not correct, since the value of the car after one year is not 100% anymore.

tip: new price with each new year is 80% = 0.8 previous price.

what is it after 2 years?