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11.10 Solving Differential Equations

Question 8

The surface area $S$ (measured in $cm2\text{cm}^2$ ) of a particular fungus culture is observed over time $t$ (measured in hours). The growth of the culture is modeled by the differential equation

\frac{\text{d}S}{\text{d}t} = \frac{8t S^{1/2}}{\text{e}^{2t}}, \quad S \ge 0, \quad t \ge 0

Given that the initial surface area of the fungus is 9 cm² at $t = 0$ , solve this differential equation to find $S^{1/2}$ in terms of $t$ , giving your answer in the form $S^{1/2} = g(t)$ .

[6]

Hence find the equation of the horizontal asymptote to the curve with equation $S^{1/2} = g(t)$ .

[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 8

The surface area $S$ (measured in $cm2\text{cm}^2$ ) of a particular fungus culture is observed over time $t$ (measured in hours). The growth of the culture is modeled by the differential equation

\frac{\text{d}S}{\text{d}t} = \frac{8t S^{1/2}}{\text{e}^{2t}}, \quad S \ge 0, \quad t \ge 0

Given that the initial surface area of the fungus is 9 cm² at $t = 0$ , solve this differential equation to find $S^{1/2}$ in terms of $t$ , giving your answer in the form $S^{1/2} = g(t)$ .

[6]

Hence find the equation of the horizontal asymptote to the curve with equation $S^{1/2} = g(t)$ .

[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.