Skip to content

Course home

4.6 Integration (A-level only)

4.6 Integration (A-level only)

MediumHard
1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162
Question 60

A biologist is studying the population, PPP, of a specific strain of bacteria in a petri dish. The rate of change of the population is modeled by the differential equation

dPdt=3P(4−t)8 \frac{dP}{dt} = \frac{3P(4 - t)}{8} dtdP​=83P(4−t)​

where t≥0t \ge 0t≥0 is the time in hours since the start of the experiment. Initially, the population is 40 units.

a.

Solve the differential equation to show that the population at time ttt is given by

P=40e316(8t−t2)for 0<t<c P = 40 e^{\frac{3}{16}(8t - t^2)} \quad \text{for } 0 < t < c P=40e163​(8t−t2)for 0<t<c

where ccc is a constant to be found that represents the time when the population first returns to its initial value.

[5]
b.

Find the exact maximum population predicted by this model. Fully justify that your answer is a maximum.

[5]
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.

Question bank