/*! 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 41 Use a graphing utility to constr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 41

Use a graphing utility to construct a table of values for the function. Then sketch the graph of the function. $$f(x)=3 e^{x+4}$$

Short Answer

Expert verified
To graph the function \(f(x) = 3e^{x+4}\), first use a graphing utility to construct a table of values. Plot these points on a Cartesian coordinate system, then draw a smooth curve connecting these points. The graph should appear as an upward trending curve, shifted 4 units to the left and stretched vertically by a factor of 3 compared to the basic graph of \(e^x\).

Step by step solution

01

Use a Graphing Utility to Construct a Table of Values

Pick several values for \(x\), like -7, -6, -5, -4, -3, -2, and -1, and then substitute these into the function \(f(x) = 3e^{x+4}\). Use a graphing utility to compute the corresponding values of \(f(x)\). This will form the table of values.
02

Plot the Points from the Table of Values

Plot the points of the form (x, f(x)) from the table of values on a Cartesian coordinate system. Be sure to appropriately label each axis and each plotted point.
03

Sketch the Graph of the function

Use a smooth curve to connect the plotted points from step 2. The curve should start from the lower left of the coordinate system and proceed upwards and to the right, reflecting the increasing trend of an exponential function.
04

Verify the Accuracy of the Graph

The graph's shape and general direction should correspond to what is generally expected of the graph of an exponential function. The graph should pass through the points on the table of values. It should shift 4 units to the left and stretch by a factor of 3 compared to the basic exponential function \(e^x\).

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

Let \(f(x)=\log _{a} x\) and \(g(x)=a^{x},\) where \(a>1\) (a) Let \(a=1.2\) and use a graphing utility to graph the two functions in the same viewing window. What do you observe? Approximate any points of intersection of the two graphs. (b) Determine the value(s) of \(a\) for which the two graphs have one point of intersection. (c) Determine the value(s) of \(a\) for which the two graphs have two points of intersection.

A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the pack will be modeled by the logistic curve \(p(t)=\frac{1000}{1+9 e^{-0.1656 t}}\) where \(t\) is measured in months (see figure). (a) Estimate the population after 5 months. (b) After how many months will the population be \(500 ?\) (c) Use a graphing utility to graph the function. Use the graph to determine the horizontal asymptotes, and interpret the meaning of the asymptotes in the context of the problem.

The sales \(S\) (in thousands of units) of a new CD burner after it has been on the market for \(t\) years are modeled by \(S(t)=100\left(1-e^{k t}\right) .\) Fifteen thousand units of the new product were sold the first year. (a) Complete the model by solving for \(k\). (b) Sketch the graph of the model. (c) Use the model to estimate the number of units sold after 5 years.

Complete the table for the time \(t\) (in years) necessary for \(P\) dollars to triple if interest is compounded annually at rate \(r\). $$ \begin{array}{|l|l|l|l|l|l|l|} \hline r & 2 \% & 4 \% & 6 \% & 8 \% & 10 \% & 12 \% \\ \hline t & & & & & & \\ \hline \end{array} $$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log (x+4)-\log x=\log (x+2)$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

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.