The value of a car, £V, is given by V = 16500 × 0.82ⁿ where n is the number of years after it is bought from new - OCR - GCSE Maths - Question 12 - 2018 - Paper 1

The formula for the value of the car is:

$V = 16500 × 0.82^n$

The value of the car decreases by a factor of 0.82 each year. To find the annual percentage decrease, we calculate:

$ext{Percentage decrease} = (1 - 0.82) × 100 = 0.18 × 100 = 18\%$

Thus, the annual percentage decrease in the value of the car is 18%.

Firstly, we calculate the value of the car after 4 years using the formula:

$V = 16500 × 0.82^4$

Calculating this:

$0.82^4 ≈ 0.4524$

Now substitute this back into the equation:

$V ≈ 16500 × 0.4524 ≈ 7465.95$

Next, we find half the value when new:

$\text{Half of £16500} = 8250$

Now we compare:

Since 7465.95 < 8250, we can conclude that the value of the car after 4 years is indeed less than half its value when new.