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1.9.31 Formulate first order differential equations (A-level only)

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Question 1

57%

The annual rate of increase of a population is equal to 2% of the size of the population. $y\,$ is the population in millions and $t\,$ is the time in years.

Write down a differential equation for this relationship

[2]

Show that $y = Ae^{0.02t}$ where $A\,$ is a constant

[4]

Given that the initial population is 2.5 million. Find the population after 10 years.

[2]

Markscheme

1.9.31 Formulate first order differential equations (A-level only) Questions

A Level
Maths
1.9.31 Formulate first order differential equations (A-level only)

50 exam-style questions on OCR (MEI) A Level Maths 1.9.31 Formulate first order differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.9.31 Formulate first order differential equations (A-level only)

Question bank

1.9.31 Formulate first order differential equations (A-level only)

Medium Hard

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Question 1

57%

The annual rate of increase of a population is equal to 2% of the size of the population. $y\,$ is the population in millions and $t\,$ is the time in years.

Write down a differential equation for this relationship

[2]

Show that $y = Ae^{0.02t}$ where $A\,$ is a constant

[4]

Given that the initial population is 2.5 million. Find the population after 10 years.

[2]

Markscheme

1.9.31 Formulate first order differential equations (A-level only) Questions

A Level
Maths
1.9.31 Formulate first order differential equations (A-level only)

50 exam-style questions on OCR (MEI) A Level Maths 1.9.31 Formulate first order differential equations (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.