John bought a new car in 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 1/4th of the price of a new car?
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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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