A magazine says that a new car's value drops by 30% in the first year. The car's value then drops by 15% each year after that. Greg says "That means the value of a new car is halved in 3 years." Is Greg correct? Justify your answer.

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Answer 1 · 2017-11-20T19:51:47

Yes.

let #x# be the cost of the car when new.

After one year the value drops by #30%#. The value at the start of the second year will be:

#(70)/100x#

The second year the value drops by #15%#. The value at the start of the third year will be:

#85/100*(70)/100x#

In the third year the value drops by #15%#. The value at the end of the third year will be:

#85/100*85/100*(70)/100x=505750/100^3x=2023/4000x=0.50575x=50.58/100x#
#->=50.57%# of #x#

This is very close to #50%#, so the answer is yes.