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Date May 2014 Marks available 3 Reference code 14M.1.sl.TZ1.11
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 11 Adapted from N/A

Question

The amount of electrical charge, C, stored in a mobile phone battery is modelled by C(t)=2.52t, where t, in hours, is the time for which the battery is being charged.



 

Write down the amount of electrical charge in the battery at t=0.

[1]
a.

The line L is the horizontal asymptote to the graph.

Write down the equation of L.

[2]
b.

To download a game to the mobile phone, an electrical charge of 2.4 units is needed.

Find the time taken to reach this charge. Give your answer correct to the nearest minute.

[3]
c.

Markscheme

1.5     (A1)     (C1)

[1 mark]

a.

C=2.5   (accept y=2.5)     (A1)(A1)     (C2)

 

Notes: Award (A1) for C (or y)= a positive constant, (A1) for the constant =2.5.

     Answer must be an equation.

 

[2 marks]

b.

2.4=2.52t     (M1)

 

Note: Award (M1) for setting the equation equal to 2.4 or for a horizontal line drawn at approximately C=2.4.

     Allow x instead of t.

 

OR

tln(2)=ln(0.1)     (M1)

t=3.32192     (A1)

t=3 hours and 19 minutes (199 minutes)     (A1)(ft)     (C3)

 

Note: Award the final (A1)(ft) for correct conversion of their time in hours to the nearest minute.

 

[3 marks]

c.

Examiners report

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

Syllabus sections

Topic 6 - Mathematical models » 6.7 » Use of a GDC to solve equations involving combinations of the functions above.
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