College Algebra, Chapter 1, 1.1, Section 1.1, Problem 100

Suppose that the average daily food consumption $F$ of a herbivorous mammal with body weight $x$, where both $F$ and $x$ are measured in pounds, is given approximately by the equation $F = 0.3x^{\frac{3}{4}}$. Find the weight $x$ of an elephant that consumes 300lb of food for day.

Let $F$ be the daily food consumption,
$x$ be the weight of an elephant.

Equation $\Longrightarrow F = 0.3x^{\frac{3}{4}}$
$F = 300$lbs.

$\begin{equation} \begin{aligned} \frac{300\text{lbs}}{0.3} &= \frac{\cancel{0.3}x^{\frac{3}{4}}}{\cancel{0.3}} && \text{Divide both sides by 0.3}\\ \\ x^{\frac{3}{4}} &= 1000 \text{lbs} && \text{Raise both sides by }\frac{4}{3}\\ \\ \left( x^{\frac{3}{4}} \right)^{\frac{4}{3}} &= (1000)^{\frac{4}{3}}\text{lbs} && \text{Simplify}\\ \\ x &= \left[ (10^3)^{\frac{1}{3}} \right]^4\text{lbs} && \text{Simplify}\\ \\ x &= (10)^4 \text{lbs} && \text{Simplify}\\ \\ x &= 10,000\text{lbs} \end{aligned} \end{equation}$

The weight of the elephant which consumes 300lb of food per day is 10,000 lbs.