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Date November 2014 Marks available 2 Reference code 14N.1.sl.TZ0.13
Level SL only Paper 1 Time zone TZ0
Command term Write down Question number 13 Adapted from N/A

Question

A potato is placed in an oven heated to a temperature of 200°C.

The temperature of the potato, in °C, is modelled by the function p(t)=200190(0.97)t, where t is the time, in minutes, that the potato has been in the oven.

Write down the temperature of the potato at the moment it is placed in the oven.

[2]
a.

Find the temperature of the potato half an hour after it has been placed in the oven.

[2]
b.

After the potato has been in the oven for k minutes, its temperature is 40°C.

Find the value of k.

[2]
c.

Markscheme

For parts (a) and (b) only, the first time a correct answer has incorrect or missing units, the final (A1) is not awarded.

200190(0.97)0     (M1)

Note: Award (M1) for correct substitution.

 

=10C     (A1)     (C2)

Note: Units are required.

a.

For parts (a) and (b) only, the first time a correct answer has incorrect or missing units, the final (A1) is not awarded.

200190(0.97)30     (M1)

Note: Award (M1) for correct substitution.

 

=124(123.808C)     (A1)     (C2)

Note: Units are required, unless already omitted in part (a).

b.

200190(0.97)k=40     (M1)

Note: Award (M1) for correct substitution.

 

k=5.64 (minutes) (5.64198)     (A1)     (C2)

c.

Examiners report

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

Syllabus sections

Topic 6 - Mathematical models » 6.4 » Exponential models.
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