On 1st November 2015 there were 4200 trees planted in a wood - OCR - GCSE Maths - Question 10 - 2017 - Paper 1

To show that $r = 0.94$, we can use the data from the first and second years. The number of trees alive after 1 year is 3948.

Substituting into the formula: $3948 = 4200r^1$

Dividing both sides by 4200 gives: $r = \frac{3948}{4200} \approx 0.94.$

Thus, it is established that $r = 0.94$.

To predict the number of trees still alive on 1st November 2030, we find $t$:

From 2015 to 2030 is 15 years, hence $t = 15$.

Using the value of $r$:

$N = 4200(0.94)^{15}$

Calculating: $N = 4200 \times (0.94)^{15} \approx 1680.$

To find the decrease in percentage:

Initial number: $4200$, Final number: $1680$.

Percentage decrease is calculated as: $\text{Percentage Decrease} = \frac{4200 - 1680}{4200} \times 100 \approx 60\%.$

Thus, we conclude that on 1st November 2030, the number of trees still alive is predicted to have decreased by over 60%.