QCEVault

Differential equations — Question 143

Original QCE Vault practice · 6 marks

Q143 · Practice questionTechnology-activeComplex unfamiliar6 marks

QUESTION 143 (6 marks)

A population satisfies dPdt=0.4P(1−P80)\frac{\mathrm{d}P}{\mathrm{d}t}=0.4P(1-\frac{P}{80}), with P(0)=20P(0)=20.
Original diagram for Specialist Mathematics Paper 2 question 14
a)
State the equilibria and their stability for positive PP.
[2 marks]
b)
Solve for P(t)P(t).
[3 marks]
c)
Find the limiting population.
[1 mark]
Question linkSyllabus coverage

Related questions

  1. Q71 · Original practice · 1 mark
    The curve x2+xy+2y2=8x^2+xy+2y^2=8 passes through (2,1)(2,1). The gradient there is
    Differential equations
  2. Q73 · Original practice · 1 mark
    The volume of a sphere is increasing at 36π cm3 s−136\pi\ \mathrm{cm^3\,s^{-1}}. When the radius is 3 cm3\ \mathrm{cm}, dr/dtdr/dt is
    Differential equations
  3. Q74 · Original practice · 5 marks
    The curve x2y+y3=10x^2y+y^3=10 passes through (1,2)(1,2).
    Differential equations
  4. Q75 · Original practice · 1 mark
    The solution of dy/dx=2xydy/dx=2xy with y(0)=3y(0)=3 has y(1)y(1) equal to
    Differential equations