2.16: Bacteria model with constants P and Q — parts (b), (c)

0606/22/O/N/20 — Question 10 · 4 marks · Exponentials, Population models

Continues Question 2.15 with the same model $b = P + Qe^{2t}$ .

Using

b = P + Qe^{2t}

with

Q = \dfrac{100}{e^{2} - 1} \approx 15.7

and

P = 500 - Q \approx 484

from part (a):

(b)

Find the number of bacteria present after

2

weeks.

[1]

(c)

Find the first week in which the number of bacteria is greater than

1\,000\,000

[3]