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4.6 Integration (A-level only)

4.6 Integration (A-level only)

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Question 48

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=0.4P2

Initially, 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.

a.

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+15​
[5]
b.

Determine the rate of change of the population when t=2t = 2t=2.

[2]
Markscheme

4.6 Integration (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4.6 Integration (A-level only)

92 exam-style questions on WJEC A Level Maths 4.6 Integration (A-level only), covering 4.6.1 Integration (A-level only) and 4.6.2 Integration (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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