| Date | May 2010 | Marks available | 2 | Reference code | 10M.1.sl.TZ2.12 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 12 | Adapted from | N/A |
Question
A rumour spreads through a group of teenagers according to the exponential model
\(N = 2 \times {(1.81)^{0.7t}}\)
where N is the number of teenagers who have heard the rumour t hours after it is first started.
Find the number of teenagers who started the rumour.
Write down the number of teenagers who have heard the rumour five hours after it is first started.
Determine the length of time it would take for 150 teenagers to have heard the rumour. Give your answer correct to the nearest minute.
Markscheme
N = 2 × (1.81)0.7×0 (M1)
N = 2 (A1) (C2)
Notes: Award (M1) for correct substitution of t = 0.
Award (A1) for correct answer.
[2 marks]
16.0 (3 s.f) (A1) (C1)
Note: Accept 16 and 15.
[1 mark]
150 = 2 × (1.81)0.7t (M1)
t = 10.39... h (A1)
t = 624 minutes (A1)(ft) (C3)
Notes: Accept 10 hours 24 minutes. Accept alternative methods.
Award last (A1)(ft) for correct rounding to the nearest minute of their answer.
Unrounded answer must be seen so that the follow through can be awarded.
[3 marks]
Examiners report
Parts (a) and (b) were confidently answered with many candidates correctly finding the number who started the rumour and also the number involved after 5 hours. A common mistake was to let t = 0 but not evaluate the expression correctly.
Parts (a) and (b) were confidently answered with many candidates correctly finding the number who started the rumour and also the number involved after 5 hours. A common mistake was to let t = 0 but not evaluate the expression correctly.
Very few candidates could answer part (c). With the working shown, it was obvious candidates could correctly state the equation, but could not use their calculators to find the value of t.
