/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 Graph each function by making a ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 18

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. $$f(x)=(0.8)^{x}$$

Short Answer

Expert verified
The graph of the function \(f(x)=(0.8)^{x}\) is a decreasing curve through the points (-2, \( (0.8)^{-2}\) ), (-1, \( (0.8)^{-1}\) ), (0, \( (0.8)^0\) ), (1, \( (0.8)^1\) ), (2, \( (0.8)^2\) ).

Step by step solution

01

Create a Table of Coordinates

Choose some x values and calculate the corresponding y values (i.e., the \(f(x)\) values). For example, let's choose -2, -1, 0, 1, 2. Then calculate \(f(-2) = (0.8)^{-2}\), \(f(-1) = (0.8)^{-1}\), \(f(0) = (0.8)^0\), \(f(1) = (0.8)^1\), and \(f(2) = (0.8)^2\). Record these in a table.
02

Plot the points and Graph the Function

Plot the points (-2, \( (0.8)^{-2}\) ), (-1, \( (0.8)^{-1}\) ), (0, \( (0.8)^0\) ), (1, \( (0.8)^1\) ), (2, \( (0.8)^2\) ) on the Cartesian plane. Join the points to draw the graph.
03

Confirm Graph using a Graphing Utility

Input the function \(f(x)=(0.8)^{x}\) into a graphing utility software and compare the resultant graph with the hand-drawn graph. Check that they match to confirm.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Rewrite the equation in terms of base \(e\). Express the answer in terms of a natural logarithm and then round to three decimal places. $$y=2.5(0.7)^{x}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\).

Find all zeros of \(f(x)=x^{3}+5 x^{2}-8 x+2\)

From 1970 through \(2010 .\) The data are shown again in the table. Use all five data points to solve Exercises \(70-74\). $$\begin{array}{cc}\hline \begin{array}{c}x, \text { Number of Years } \\\\\text { after } 1969 \end{array} & \begin{array}{c}y, \text { U.S. Population } \\\\\text { (millions) }\end{array} \\ \hline 1(1970) & 203.3 \\\11(1980) & 226.5 \\\21(1990) & 248.7 \\\31(2000) & 281.4 \\\41(2010) & 308.7 \end{array}$$ Use your graphing utility's linear regression option to obtain a model of the form \(y=a x+b\) that fits the data. How well does the correlation coefficient, \(r,\) indicate that the model fits the data?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. After 100 years, a population whose growth rate is \(3 \%\) will have three times as many people as a population whose growth rate is \(1 \%\)
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.