O-LevelAdditional MathematicsLogarithmic and exponential functions4037/11 · May/June 2018 · Q56 Marks
The population, P, of a certain bacterium t days after the start of an experiment is modelled by P = 800e^(kt), where k is a constant.
- (i)State what the figure 800 represents in this experiment.[1]
- (ii)Given that the population is 20000 two days after the start of the experiment, calculate the value of k.[3]
- (iii)Calculate the population three days after the start of the experiment.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] The number of bacteria at the start of the experiment
- [M1] use of given equation and attempt to solve for e^(2k) or use logs correctly
- [M1] correct method to obtain 2k
- [A1] 1.61
- [M1] Substitution of t = 3 in formula using their k
- [A1] answer in range 99800 to 100200
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