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1.2.12 The modulus function (A-level only)

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Question 21

The strength of a radio signal SSS, measured in microvolts, is modelled by the function

S(t)=32∣2t−10∣+4,t⩾0 S(t) = \frac{3}{2}|2t - 10| + 4, \quad t \geqslant 0 S(t)=23​∣2t−10∣+4,t⩾0

where t t\,t is the time in seconds after a broadcast begins. The minimum signal strength occurs at point VVV.

a.

Determine the coordinates of VVV.

[2]
b.

Solve the equation S(t)=t+7S(t) = t + 7S(t)=t+7.

[3]
c.

An interference signal is modelled by the equation

S(t)=mt+1 S(t) = mt + 1 S(t)=mt+1

where m m\,m is a constant. Given that the broadcast signal and the interference signal have equal strength at exactly two distinct times,

find the range of possible values for mmm.

[4]

1.2.12 The modulus function (A-level only) Questions

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