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Cycle 2 - Lesson 3 – Reciprocal Functions - Modelling and Applications Steps to model a linear reciprocal function: (from Desmos activity) General equation:

Application #1 – Diving Time The maximum time, T, in minutes, a scuba diver can rise without stopping for decompression on the way up to the surface is defined by the equation

T (d ) 

525 ,d  0 d  10

where d is the depth of the dive, in metres.

For the maximum time to be less than 30 minutes, how deep can the diver dive?

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Application #2 – Intensity of Sound Most of us know that getting closer to a concert stage means getting a better view, but it also means more exposure to potentially damaging sound levels.

The intensity, I, increases by what is known as the inverse square law, or the _____________________ of the square of the distance, d, from the sound source.

This law also applies to _______________________ force and ______________ intensity.

Example: The intensity of sound, in watts per square metre, varies inversely as the square of the distance, in metres, from the source of the sound. The intensity of the sound from a loudspeaker at a distance of 2 metres is 0.001 W/m2.

a)

Determine the value of the constant k for this situation in the general equation for sound intensity:

I

b)

k d2

Graph this function on Desmos, restricting the domain based on this context. Sketch of graph:

c) What is the effect of halving the distance from the source of the sound?

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C2-L3 – Practice Questions

3.

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Answers to practice questions

3.

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