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Chapter 7: Problem 42

What is an exponential function?

Short Answer

Expert verified
An exponential function is a mathematical function of the form \(y = ab^x\), where \(a\) and \(b\) are constants, \(b\) is positive and not equal to 1, and \(x\) is the variable (exponent). It especially reflects quantities that increase or decrease rapidly and consistently.

Step by step solution

01

General Form

An exponential function can be represented in a general form as: \(y = ab^x\) where \(a\) and \(b\) are constants, \(b\) is positive and not equal to 1, and \(x\) is the variable (exponent).
02

When base is greater than one

If \(b > 1\) , the function continuously increases in value as \(x\) increases. This represents growth and is often used in calculations involving interest rates, population sizes, radioactive decay etc.
03

When base is between zero and one

If \(0 < b < 1\) , the function continuously decreases in value as \(x\) increases. This represents decay and is often used in describing depreciation, cooling of objects, discharging of capacitors etc.

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Most popular questions from this chapter

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{r}2 x+y<3 \\ x-y>2\end{array}\right.\)

Without graphing, Determine if each system has no solution or infinitely many solutions. \(\left\\{\begin{array}{l}6 x-y \leq 24 \\ 6 x-y>24\end{array}\right.\)

Graph each linear inequality. \(y \leq 3 x+2\)

Graph each linear inequality. \(2 x+3 y>12\)

Graph the solution set of each system of inequalities. \(\left\\{\begin{array}{l}x-y \leq 1 \\ x \geq 2\end{array}\right.\)
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