John bought a new car at the start of the year 2015 and from that moment on the
value of its car is continuously dropping. At the end of each year the value have
dropped for 12.5% in compare to the value at start of that year. During what year will
the value of the car for the first time be less than 1th of the price of a new car?
Answers
Given: John bought a new car in 2015 . At the end of each year the value have dropped for 12.5% in compare to the value at start of that year.
To Find : During what year will the value of the car for the first time be less than 1/4th of the price of a new car?
Solution:
John bought a new car in 2015
Let say Price of Car = P
Car Price after 1 year = P - (12.5/100)P = 0.875P
Car Price after 2 year = 0.875P - (12.5/100)0.875P = 0.875P(0.875)
= 0.875²P
Car Price after n years = 0.875ⁿP
value of the car for the first time be less than 1/4th of the price of a new car
0.875ⁿP < P/4
=> 0.875ⁿ < 1/4
=> n log (0.875) < log (1/4)
=> n(-0.058) < -0.6
=> n > 0.6/0.058
=> n > 10.34
=> n = 11
After 11 years the value of the car for the first time be less than 1/4th of the price of a new car
in 12th Year the value of the car for the first time be less than 1/4th of the price of a new car
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