Higher November 2021 Paper 4 Q16
16 The formula
\[P = 6800 \times 1.045^n\]is used to predict the population, \(P\), of an island \(n\) years after 2018.
(a) Write down the population of the island in 2018. [1]
(b) Write down the percentage growth rate used in the formula. [1]
(c)
(i) Work out the population predicted by the formula for the year 2030. [2]
(ii) Give one reason why the answer to (c)(i) may not be reliable. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 6800 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 4.5 | 1 | condone extra % | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) 11500 or 11530 or 11532 | 2 | M1 for \(6800 \times 1.045^{12}\) oe | allow 11531 and 11531.9[9…] |
| (ii) Any correct reason e.g. the rate may not continue | 1 | see appendix | |
Appendix: exemplar responses for Q16(c)(ii)
| Response | Mark |
|---|---|
| the rate may not continue | 1 |
| there may not be enough housing on the island | 1 |
| they may run out of space | 1 |
| there may be a famine | 1 |
| people may move | 1 |
| there may be disease | 1 |
| the answer is a decimal | 0 |
| people will die | 0 |