The Galdpagos Islands, lying 600 miles west of Ecuador, are...

The Galdpagos Islands, lying 600 miles west of Ecuador, are famed for their extraordinary wildlife. The function $$ f(x)=29 x^{5} $$ models the number of plant species, $f(x),$ on the various islands of the Galdpagos chain in terms of the area, $x,$ in square miles, of a particular island. Use the function to solve Exercises $125-126$ How many species of plants are on a Galápagos island that has an area of 8 square miles?

The Galdpagos Islands, lying 600 miles west of Ecuador, are famed for their extraordinary wildlife. The function
$$
f(x)=29 x^{5}
$$
models the number of plant species, $f(x),$ on the various islands of the Galdpagos chain in terms of the area, $x,$ in square miles, of a particular island. Use the function to solve
Exercises $125-126$
How many species of plants are on a Galápagos island that has an area of 8 square miles?

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Key Concepts

Function Evaluation

Function evaluation involves substituting a given value into a function to determine the corresponding output. In real-world problems, this technique is used to calculate specific quantities based on a model, such as determining the number of species on an island by plugging the island's area into the function.

Power Functions

A power function is a type of function where the variable is raised to a constant exponent. This form is frequently used in modeling natural phenomena because it captures nonlinear relationships, where small changes in the independent variable can lead to larger changes in the output.

Mathematical Modeling

Mathematical modeling is the process of using mathematical formulas to represent complex real-world systems and phenomena. In this context, the function f(x) = 29x^5 is used to model how the number of plant species on an island varies with the island's area.

Exponentiation

Exponentiation involves raising a number to a certain power, which is a fundamental operation in algebra. This concept is essential when working with power functions, as the exponent determines the rate at which the function’s output grows with respect to its input.

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