Question

CRITICAL THINKING The weight y (in pounds) of a rainbow trout can be modeled by y = 0.000304x3, where x is the length (in inches) of the trout. a. Write a function that relates the weight y and length x of a rainbow trout when y is measured in kilograms and x is measured in centimeters. Use the fact that 1 kilogram ≈ 2.20 pounds and 1 centimeter ≈ 0.394 inch.

Answer 1

`y = 0.01092395604x^3`

Explanation:

Given:

`y = 0.000304x^3`

Where y is in pounds and x is in inches

Required

Represent y in kilogram and x in centimetre

`y = 0.000304x^3`

The expression can be rewritten as

`(y\ pound) = 0.000304(x\ inch)^3`

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If
`0.394\ inch= 1\ cm`

Divide both by 0.394

`(0.394\ inch)/(0.394)= (1\ cm)/(0.394)`

`1\ inch= (1\ cm)/(0.394)`

`1\ inch = 2.538\ cm` (Approximated)

Multiply both sides by x

`x * 1\ inch = 2.538\ cm * x`

`x \ inch = 2.538x\ cm`

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If
`2.20\ pound = 1\ kg`

Divide both by 2.20

`(2.20\ pound)/(2.20) = (1\ kg)/(2.20)`

`1\ pound = (1\ kg)/(2.20)`

`1\ pound = 0.455\ kg` (Approximated)

Multiply both sides by y

`y * 1\ pound = 0.454\ kg * y`

`y \ pound = 0.454y\ kg`

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Substitute 0.455y kg for y pound and 2.538x cm for x inch in
`(y\ pound) = 0.000304(x\ inch)^3`

`0.454y = 0.000304(2.538x)^3`

`0.454y = 0.000304(16.35x^3)` Approximated

`0.454y = 0.0049704x^3`

Divide both sides by 0.455

`(0.455y)/(0.455) = (0.0049704x^3)/(0.455)`

`y = (0.0049704x^3)/(0.455)`

`y = 0.01092395604x^3`