# Proportional relationships

Assume that male snakes of a particular species are all scaled versions of the same basic shape.

(i) (a) Describe in words the sort of relationship that you might expect there to be between the volume and the length of a snake. What relationship would you expect there to be between the mass and the length of a snake ?.

(b) If the mass (in grams) is denoted by M and the length (in cm) is denoted by L, write down a proportional relationship for M in terms of L.

(c) Rearrange this relationship to find a proportional relationship for L in terms of M Hence, write down a power law relationship for L in terms OF M, Using K as the constant of proportionality.

(iii) (a) A snake sheds its skin periodically; this is a process known as sloughing. Denoting the area of the shed skin as A (in cm^2), find a proportional relationship for A in in terms of M.

(b) The skin area of a particular snake of mass 64g is approximately 270cm^2 Use this information to estimate the constant of proportionality for the power law for A in terms of M ,

Hence, estimate the approximate skin area for a snake of mass 200g.

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Solution.

(i) (a) By observation of its shape, i think the relationship between the volume and its length might be linear, that is, the longer the bigger volume. Similarly, there is a linear ...

#### Solution Summary

The main aims of this question are to:

1,Use proportional relationships in relevant contexts.

2,Explain the meaning of, and use correctly, words describing proportional relationships.

3,Write down proportional relationships both in the from of a power equation and as an expression involving the proportion symbol x.

4, Use power regression to test proportional relationships.

5, Manipulate proportional relationships in practical contexts.