A biological culture is treated with a disinfectant. The population of bacteria, PPP, in thousands, decreases at a rate modeled in terms of its current population by the equation:
Rate of decrease=0.4P2 \text{Rate of decrease} = 0.4P^2 Rate of decrease=0.4P2Initially, the population of the culture is 5000 bacteria, so P=5P = 5P=5 at t=0t = 0t=0, where ttt is the time in hours after the disinfectant is applied.
By first forming a suitable differential equation involving dPdt\frac{dP}{dt}dtdP, show that
P=52t+1 P = \frac{5}{2t + 1} P=2t+15Determine the rate of change of the population when t=2t = 2t=2.
864 exam-style questions on Edexcel A Level Maths Integration, 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. Each one has a worked solution and a mark scheme showing where the marks go.