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

To find the annual percentage decrease, we look at the factor by which the value decreases each year. From the formula, each year the value of the car is multiplied by 0.82.

The annual percentage decrease is given by:

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

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

First, we calculate the value of the car after 4 years by substituting n = 4 into the formula:

$V = 16500 × 0.82^4$

Calculating this gives:

$V = 16500 × 0.4506 ≈ 7439.85$

Now, half of the initial value when new is:

$\frac{16500}{2} = 8250$

We see that:

$7439.85 < 8250$

Thus, the value of the car after 4 years is indeed less than half its value when new.