Higher November 2020 Paper 2 Q25
25.
(a) The number of voles, \(V\), on an island \(t\) years after the first voles are introduced is given by the formula
\(V=135\times1{\cdot}06^t\).
(i) How many voles were initially introduced? [1]
(ii) What is the percentage increase in the number of voles 5 years after they were introduced? [2]
(iii) When the number of voles reaches 500, the population starts decreasing at a rate of 5% per month.
The formula \(V=500\times k^T\) is now used to model the number of voles, \(V\),
where \(T\) is the number of years after the population reached 500.
What value of \(k\) should be used? [1]
The formula \(V=500\times k^T\) is now used to model the number of voles, \(V\),
where \(T\) is the number of years after the population reached 500.
What value of \(k\) should be used? [1]
(b) A population of birds on the island has a constant growth rate, \(p\)%, per year.
There were initially 300 birds.
The population doubles in 20 years.
Calculate the value of \(p\). [3]
There were initially 300 birds.
The population doubles in 20 years.
Calculate the value of \(p\). [3]
| Scheme | Marks | Comments |
|---|---|---|
| (a)(i) | ||
| 135 | B1 | |
| (a)(ii) | ||
| 33 or 33.8 or 34 | B2 | Award B2 for answers of 32.59(…) or 32.6 from working year by year and rounding down to a whole number. B1 for any one of the following seen
|
| (a)(iii) | ||
| 0.54(…) | B1 | |
| Scheme | Marks | Comments |
|---|---|---|
| \(\left(1+\dfrac{p}{100}=\right)\ \sqrt[20]{2}\) or 1.03526... | B2 | Allow B2 for \(p=\sqrt[20]{2}\) or \(p\) = 1.03(52…) B1 for \((300\times)\left(1+\dfrac{p}{100}\right)^{20}=2(300)\) or \(x^{20}=2\) Allow B1 for \(p^{20}=2\) |
| 3.5(26…) | B1 | |
| (7) |