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Date May 2019 Marks available 2 Reference code 19M.2.SL.TZ2.S_5
Level Standard Level Paper Paper 2 Time zone Time zone 2
Command term Find Question number S_5 Adapted from N/A

Question

The population of fish in a lake is modelled by the function

f ( t ) = 1000 1 + 24 e 0.2 t , 0 ≤ t  ≤ 30 , where  t is measured in months.

Find the population of fish at t = 10.

[2]
a.

Find the rate at which the population of fish is increasing at t = 10.

[2]
b.

Find the value of t for which the population of fish is increasing most rapidly.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

valid approach      (M1)

eg    f (10)

235.402

235 (fish) (must be an integer)     A1 N2

[2 marks]

a.

recognizing rate of change is derivative     (M1)

eg  rate = f f (10) , sketch of f ,  35 (fish per month)

35.9976

36.0 (fish per month)     A1 N2

[2 marks]

b.

valid approach    (M1)

eg   maximum of f ,    f = 0

15.890

15.9 (months)     A1 N2

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5 —Calculus » SL 5.6—Differentiating polynomials n E Q. Chain, product and quotient rules
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Topic 5 —Calculus

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