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11.10 Solving Differential Equations

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Question 20

A biological culture is treated with a disinfectant. The population of bacteria, $P$ , in thousands, decreases at a rate modeled in terms of its current population by the equation:

\text{Rate of decrease} = 0.4P^2

Initially, the population of the culture is 5000 bacteria, so $P = 5$ at $t = 0$ , where $t$ is the time in hours after the disinfectant is applied.

By first forming a suitable differential equation involving $dPdt\frac{dP}{dt}$ , show that

\frac{5}{2t + 1}

[5]

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

[2]

Markscheme

11.10 Solving Differential Equations Questions

A Level
Maths
11.10 Solving Differential Equations

34 exam-style questions on Edexcel A Level Maths 11.10 Solving Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.

11.10 Solving Differential Equations

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11.10 Solving Differential Equations

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Question 20

A biological culture is treated with a disinfectant. The population of bacteria, $P$ , in thousands, decreases at a rate modeled in terms of its current population by the equation:

\text{Rate of decrease} = 0.4P^2

Initially, the population of the culture is 5000 bacteria, so $P = 5$ at $t = 0$ , where $t$ is the time in hours after the disinfectant is applied.

By first forming a suitable differential equation involving $dPdt\frac{dP}{dt}$ , show that

\frac{5}{2t + 1}

[5]

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

[2]

Markscheme

11.10 Solving Differential Equations Questions

A Level
Maths
11.10 Solving Differential Equations

34 exam-style questions on Edexcel A Level Maths 11.10 Solving Differential Equations. Each one has a worked solution and a mark scheme showing where the marks go.