Higher November 2021 Paper 3 Q19
19 At the start of year \(n\), the number of animals in a population is \(P_n\)
At the start of the following year, the number of animals in the population is \(P_{n + 1}\) where
\(P_{n + 1} = kP_n\)
At the start of 2017 the number of animals in the population was 4000
At the start of 2019 the number of animals in the population was 3610
Find the value of the constant \(k\). (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| 0.95 | P1 | for initial use of the formula eg \(3610 = kP_n\) or \(P_{n+1} = 4000k\) or for \(P_{n+2} = k^2 P_n\) or for \(3610 = k^2 \times 4000\) |
| P1 | for a complete method to find \(k\) eg \(\sqrt{\dfrac{3610}{4000}}\) or \(\pm 0.95\) | |
| A1 | oe |
Additional guidance
Accept \(n\) or any integer replacement for \(n\)
This may be seen in steps