Question

1. . Under a set of controlled laboratory conditions, the size of the population P of a certain bacteria culture at time t (in seconds) is given by the function P(t)= 3t²+ 3e^t+10, (t greater than/ equal to 0)

(i) What is the size of the population after 1 minute?

(ii) Find the average rate of change of P at t = 2 and t = 6?

(iii) How fast is the size of the population changing after 1 minute?

[Verify your answer by MATHEMATICA and attach the printout of the commands and output]

Answer 1

i)

$P(60)=3\cdot60^2+3e^{60}+10=3.4\cdot10^{26}$

ii)

$\frac{P(6)-P(2)}{6-2}=\frac{1328-44}{4}=321$

iii)

$P'(t)=6t+3e^t$

$P'(60)=6\cdot60+3e^{60}=3.4\cdot10^{26}$