2.16: Bacterial growth model with exponential decay term

0606/21/O/N/16 — Question 4 · 7 marks

The number of bacteria, NN, present in a culture can be modelled by the equation N=7000+2000e0.05tN = 7000 + 2000\mathrm{e}^{-0.05t}, where tt is measured in days.
(i)
Find the number of bacteria when t=10t = 10.
[1]
(ii)
Find the value of tt when the number of bacteria reaches 75007500.
[3]
(iii)
Find the rate at which the number of bacteria is decreasing after 88 days.
[3]