| Date | May 2013 | Marks available | 2 | Reference code | 13M.1.sl.TZ2.13 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Calculate | Question number | 13 | Adapted from | N/A |
Question
The number of bacteria in a colony is modelled by the function
\(N(t) = 800 \times 3^{0.5t}, {\text{ }} t \geqslant 0\),
where \(N\) is the number of bacteria and \(t\) is the time in hours.
Write down the number of bacteria in the colony at time \(t = 0\).
Calculate the number of bacteria present at 2 hours and 30 minutes. Give your answer correct to the nearest hundred bacteria.
Calculate the time, in hours, for the number of bacteria to reach 5500.
Markscheme
800 (A1) (C1)
\(800 \times {3^{(0.5 \times 2.5)}}\) (M1)
Note: Award (M1) for correctly substituted formula.
\( = 3158.57\)... (A1)
\(= 3200\) (A1) (C3)
Notes: Final (A1) is given for correctly rounding their answer. This may be awarded regardless of a preceding (A0).
\(5500 = 800 \times {3^{(0.5 \times t)}}\) (M1)
Notes: Award (M1) for equating function to 5500. Accept correct alternative methods.
\(= 3.51{\text{ hours}}\) (3.50968...) (A1) (C2)
