Skip to content
MathsGenie logo
Open app

Course home

  1. A Level
  3. Maths Edexcel
  5. Question bank

11.10 Solving Differential Equations

MediumHard
1234567891011121314
Question 8

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

dSdt=8tS1/2e2t,S≥0,t≥0 \frac{\text{d}S}{\text{d}t} = \frac{8t S^{1/2}}{\text{e}^{2t}}, \quad S \ge 0, \quad t \ge 0 dtdS​=e2t8tS1/2​,S≥0,t≥0
a.

Given that the initial surface area of the fungus is 9 cm2 at t=0t = 0t=0, solve this differential equation to find S1/2S^{1/2}S1/2 in terms of ttt, giving your answer in the form S1/2=g(t)S^{1/2} = g(t)S1/2=g(t).

[6]
b.

Hence find the equation of the horizontal asymptote to the curve with equation S1/2=g(t)S^{1/2} = g(t)S1/2=g(t).

[2]

11.10 Solving Differential Equations Questions

  1. A Level
  2. /Maths
  3. /11.10 Solving Differential Equations

Practise Edexcel A Level Maths 11.10 Solving Differential Equations with exam-style questions for A Level Maths. 35 questions, 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.

Question bank