Ch. 3 - Polynomial and Rational Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 3 - Polynomial and Rational Functions

Problem 5

Chapter 4, Problem 5

Using k as the constant of variation, write a variation equation for each situation. h varies inversely as t.

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Identify the type of variation described. Since h varies inversely as t, this means h is inversely proportional to t.

Recall the general form of an inverse variation equation: \(h = \frac{k}{t}\), where \(k\) is the constant of variation.

Write the variation equation using the given variables: \(h = \frac{k}{t}\).

Understand that \(k\) is a constant that can be determined if specific values of \(h\) and \(t\) are given, but for now, it remains as \(k\).

This equation expresses that as \(t\) increases, \(h\) decreases proportionally, and vice versa, consistent with inverse variation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inverse Variation

Inverse variation describes a relationship where one variable increases as the other decreases, such that their product is constant. Mathematically, if h varies inversely as t, then h × t = k, where k is a constant.

Constant of Variation (k)

The constant of variation, denoted by k, is a fixed value that relates two variables in a variation equation. In inverse variation, k equals the product of the two variables and remains unchanged as the variables change.

Writing Variation Equations

To write a variation equation, identify the type of variation (direct or inverse) and express the relationship using a constant. For inverse variation, the equation is h = k / t, showing how h depends on t through the constant k.

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