Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Equivalent Representations: Rational Functions, Exercise 17: Exercise 4C

Ben is a dentist. He believes there is a relationship between the average number of cavities developed in each of his patients' mouths per year $\left(y\right)$ and the number of minutes they brush their teeth each morning and evening $\left(x\right)$ Ben believes the function $y=\frac{2}{x}$ represents this relationship. Alita is Ben's patient.

Determine how many cavities Alita is likely to develop in one year if she brushes her teeth for two minutes each morning and evening.

Ben is a dentist. He believes there is a relationship between the average number of cavities developed in each of his patients' mouths per year $\left(y\right)$ and the number of minutes they brush their teeth each morning and evening $\left(x\right)$ Ben believes the function $y=\frac{2}{x}$ represents this relationship. Chamse is Ben's patient.

Chamse develops four cavities in a year. Find the number of minutes she likely spent brushing her teeth each morning and evening.

[Enter the value excluding units]

On a string instrument, the length of a string $(l \mathrm{cm})$ and the frequency of its vibrations $( v \mathrm{Hz})$ are modelled by the equation $v=\frac{1000}{l}$.

Use technology to sketch the function for $0<l\le 20$.

On a string instrument, the length of a string $(l \mathrm{cm})$ and the frequency of its vibrations $( v \mathrm{Hz})$ are modelled by the equation $v=\frac{1000}{l}$.

Find the frequency of vibrations for a string which is $10 \mathrm{cm}$ long.

[Enter the value excluding units]

Tak's phone can store $64$ videos which are each one minute long; of $32$ videos of length two minutes; or $16$ videos of length four minutes; etc.

Find the number of videos of length $16$ minutes Tak could store on his phone.

Tak's phone can store $64$ videos which are each one minute long; of $32$ videos of length two minutes; or $16$ videos of length four minutes; etc.

Find a function to represent the relationship between the number of videos on Tak's phone $x$ and the length of each video ($y$ minutes).

Tak's phone can store $64$ videos which are each one minute long; of $32$ videos of length two minutes; or $16$ videos of length four minutes; etc.

Find a function to represent the relationship between the number of videos on Tak's phone $x$ and the length of each video ($y$ minutes) and plot the graph.

Tak's phone can store $64$ videos which are each one minute long; of $32$ videos of length two minutes; or $16$ videos of length four minutes; etc.

Find a function to represent the relationship between the number of videos on Tak's phone $x$ and the length of each video ($y$ minutes) and plot the graph.

Tak wants to store $48$ videos on his phone. Plot an appropriate straight line on the same axes to help you find the maximum length of each video.