Acar is purchased for 26000. each year it loses 30% of its value. after how many years will the car be worth 2200 or less?

write the smallest possible whole number answer.

The smallest possible number of years for the depreciation value of car is 7 years .

Step-by-step explanation:

Given as :

The purchased price of car = $26000

The depreciation rate of car every year = r = 30%

The reduced price of car after n years = $2200 or less

Let The time period for the depreciation value = n years

Now, According to question

The reduced price of car after n years = The purchased price of car ×

Or, $2200 = $26000 ×

Or, =

Or, 0.084615 =

Now, Taking Log both side

So, 0.084615 =  ( )

Or, -1.07255 = n 0.7

Or, -1.07255 = n ( - 0.15490 )

∴ n =

I.e n = 6.92 ≈ 7 years

So, Time period for depreciation of car value = n = 7 years

Hence The smallest possible number of years for the depreciation value of car is 7 years . Answer