Higher November 2022 Paper 2 Q12
12 The number of insects in a population at the start of the year \(n\) is \(P_n\)
The number of insects in the population at the start of year \((n + 1)\) is \(P_{n+1}\) where
\[P_{n+1} = kP_n\]Given that \(k\) has a constant value of 1.13
(a) find out how many years it takes for the number of insects in the population to double.
You must show how you get your answer. (2)
You must show how you get your answer. (2)
The value of \(k\) actually increases year on year from its value of 1.13 in year 1
(b) How does this affect your answer to part (a)? (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 6 | M1 | for an attempt to evaluate \(1.13^n\) for at least one value of \(n\) (with \(n \gt 1\)) |
| A1 | 6 years coming from finding \(n\) such that \(1.13^n \gt 2\) |
Additional guidance
1.13, 1.27…, 1.44…, 1.63…, 1.84…, 2.08…
May be used with a value
Values rounded or truncated to 2dp or better
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for explanation Acceptable examples it will decrease the number of years will go down we can’t tell (as we don’t know how much it is increasing by) it will be an overestimate Not acceptable examples it will increase it will be an underestimate |