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

Answer:

$y = 0.01092395604x^3$

Step-by-step 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

$\frac{0.394\ inch}{0.394}= \frac{1\ cm}{0.394}$

$1\ inch= \frac{1\ cm}{0.394}$

$1\ inch = 2.538\ cm$ (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

$\frac{2.20\ pound}{2.20} = \frac{1\ kg}{2.20}$

$1\ pound = \frac{1\ kg}{2.20}$

$1\ pound = 0.455\ kg$ (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

$\frac{0.455y}{0.455} = \frac{0.0049704x^3}{0.455}$

$y = \frac{0.0049704x^3}{0.455}$

$y = 0.01092395604x^3$