Question

At the start of 2014 Mike's car was worth ?12000.The value of the car decreased by 30% every year.Work out the valure of his car at the start of 2017

Answer 1

The value of Mike's car at the start of 2017 is 4,116.

Step-by-step explanation:

The value of Mike's car at the start of 2014 was 12,000. The value of the car decreased by 30% every year. To find the value of the car at the start of 2017, we need to perform three percentage decreases on the initial value.

Step 1: Calculate the value of the car at the start of 2015: 12,000 - (30% of 12,000) = 12,000 - (0.3 x 12,000) = 12,000 - 3,600 = 8,400

Step 2: Calculate the value of the car at the start of 2016: 8,400 - (30% of 8,400) = 8,400 - (0.3 x 8,400) = 8,400 - 2,520 = 5,880

Step 3: Calculate the value of the car at the start of 2017: 5,880 - (30% of 5,880) = 5,880 - (0.3 x 5,880) = 5,880 - 1,764 = 4,116

Therefore, the value of Mike's car at the start of 2017 is 4,116.

Answer 2

$6860.

Step-by-step explanation:

We have been given that at the start of 2014 Mike's car was worth $12000.The value of the car decreased by 30% every year.

We will exponent decay formula to solve our given problem.

`y=a\cdot (1-r)^x`, where,

y = Final value,

a = Initial value,

r = Decay rate in decimal form.

`30\%=(30)/(100)=0.30`

Initial value of car is $12000.

3 years from 2014 to 2017.

`y=20,000\cdot (1-0.30)^3`

`y=20,000\cdot (0.70)^3`

`y=20,000\cdot 0.343`

`y=6860`

Therefore, the value of car at the start of year 2017 would be $6860.