Question

George just bought a new scooter for $8000. He plans on keeping it until it is worth a fourth of it's original price.

He believes that every year the scooter loses an eighth of its value. He can represent the value of the scooter by the equation V = 8000(7/8)t, where V is the value of the scooter and t is the number of years that have passed.

As he was leaving the dealership he was told that the scooter really loses a sixth of it's value every year. What should George change in the equation V = 8000(7/8)t to represent this new situation?


A) Replace the 7/8 with a 6.
B) Replace the 8000 with 5/6.
C) Switch the V and t
D) Replace the 7/8 with a 5/6.

Answer 1

since it's 1/6th and not 1/8th then replace 7/8 with a 5/6

Answer 2

D) Replace the 7/8 with a 5/6.

Explanation:

Given,

The original value of the scooter = $ 8000,

If it loses an eighth of its value.

Then the decrement in the price of scooter =
`(1)/(8)` of the original price of the scooter

`=(1)/(8)* 8000`

`=(8000)/(8)`

Now, the final price of the scooter = Original price of the scooter - Decrement in price

`=8000-(8000)/(8)`

`=8000(1-(1)/(8))`

`=8000((8-1)/(8)`

`=8000((7)/(8))`

Similarly, If it loses an sixth of its value.

Then, decrement in price =
`(1)/(6)` of 8000

`=(8000)/(6)`

And, the final price of the scooter =
`8000-(8000)/(6)`

`=8000(1-(1)/(6))`

`=8000((6-1)/(6))`

`=8000((5)/(6))`

Hence, Option D is correct.