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​Q16: Paper 1 – November 2023

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Question

16)

At the start of year n the population of a species is P_n

At the start of the following year the population of the species is given by

P_n+1 = kP_n where k is a positive constant.

 

The population of the species at the start of year 1 is 8 million.

The population of the species at the start of year 2 is 6 million.

(a) Work out the population of the species at the start of year 3

[3 marks]
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At the start of year 5 the value of k is increased by 0.3 to a new constant value.

Louise thinks that from the start of year 5 the population of the species would increase year on year.

(b) Is Louise correct?

You must give a reason for your answer.

[2 marks]

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Mark Scheme

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Working

16)

At the start of year n the population of a species is P_n

At the start of the following year the population of the species is given by

P_n+1 = kP_n where k is a positive constant.

 

The population of the species at the start of year 1 is 8 million.

The population of the species at the start of year 2 is 6 million.

(a) Work out the population of the species at the start of year 3

There is no working for part b