| Date | May 2014 | Marks available | 1 | Reference code | 14M.2.sl.TZ1.5 |
| Level | SL only | Paper | 2 | Time zone | TZ1 |
| Command term | Interpret | Question number | 5 | Adapted from | N/A |
Question
The population of deer in an enclosed game reserve is modelled by the function \(P(t) = 210\sin (0.5t - 2.6) + 990\), where \(t\) is in months, and \(t = 1\) corresponds to 1 January 2014.
Find the number of deer in the reserve on 1 May 2014.
Find the rate of change of the deer population on 1 May 2014.
Interpret the answer to part (i) with reference to the deer population size on 1 May 2014.
Markscheme
\(t = 5\) (A1)
correct substitution into formula (A1)
eg \(210\sin (0.5 \times 5 - 2.6) + 990,{\text{ }}P(5)\)
\(969.034982 \ldots \)
969 (deer) (must be an integer) A1 N3
[3 marks]
evidence of considering derivative (M1)
eg \(P'\)
\(104.475\)
\(104\) (deer per month) A1 N2
[2 marks]
(the deer population size is) increasing A1 N1
[1 mark]
