A population of bacteria in a laboratory culture is being monitored. The number of bacteria, BBB, in the culture, t t\,t hours after the initial observation, is modelled by the equation
B=400ekt7+ekt B = \frac{400e^{kt}}{7 + e^{kt}} B=7+ekt400ektwhere k k\,k is a constant.
Find the number of bacteria in the culture at the start of the study.
Given that there are 160 bacteria in the culture after 5 hours,
show that k=15ln(143)\displaystyle k = \frac{1}{5}\ln\left(\frac{14}{3}\right)k=51ln(314).
Given also that, when t=Tt = Tt=T, the number of bacteria is increasing at a rate of 25 per hour,
find the possible values of TTT, giving your answers to one decimal place.
Practise Edexcel A Level Maths Integration with exam-style questions for A Level Maths. 437 questions covering 11.1 Integrating Standard Functions, 11.2 Integrating f(ax + b), 11.3 Using Trigonometric Identities, 11.4 Reverse Chain Rule, 11.5 Integration by Substitution, 11.6 Integration by Parts, 11.7 Partial Fractions, 11.8 Finding Areas, 11.9 The Trapezium Rule, 11.10 Solving Differential Equations, and 11.11 Modelling with Differential Equations, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
