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Date May 2019 Marks available 2 Reference code 19M.1.SL.TZ2.T_13
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 2
Command term Find and Justify Question number T_13 Adapted from N/A

Question

Little Green island originally had no turtles. After 55 turtles were introduced to the island, their population is modelled by

N(t)=a×2t+10,t0,

where a is a constant and t is the time in years since the turtles were introduced.

 

Find the value of a.

[2]
a.

Find the time, in years, for the population to decrease to 20 turtles.

[2]
b.

There is a number m beyond which the turtle population will not decrease.

Find the value of m. Justify your answer.

[2]
c.

Markscheme

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

55=a×20+10   (M1)

Note: Award (M1) for correct substitution of zero and 55 into the function.

45      (A1)   (C2)  

[2 marks]

a.

45×2t+1020       (M1)

Note: Award (M1) for comparing correct expression involving 20 and their 45. Accept an equation.

t=2.17  (2.16992…)      (A1)(ft)   (C2)

Note: Follow through from their part (a), but only if positive.
Answer must be in years; do not accept months for the final (A1).  

[2 marks]

b.

m=10       (A1)

because as the number of years increases the number of turtles approaches 10      (R1)   (C2)

Note: Award (R1) for a sketch with an asymptote at approximately y=10,
OR for table with values such as 10.003 and 10.001 for t=14 and t=15, for example,
OR when t approaches large numbers y approaches 10. Do not award (A1)(R0). 

[2 marks]

c.

Examiners report

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

Syllabus sections

Prior learning
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