/*! 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 33 Use a calculator to find each of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 33

Use a calculator to find each of the following to four decimal places. $$ e^{-3.49} $$

Short Answer

Expert verified
0.0305

Step by step solution

01

Understand the problem

The task is to find the value of the mathematical expression \(e^{-3.49}\) using a calculator. The result should be accurate to four decimal places.
02

Input the expression into the calculator

Turn on the calculator and ensure it is in standard mode. Input the expression \(e^{-3.49}\) into the calculator. Most scientific calculators have an \(e^x\) button that can be used for this purpose. Press the \(e^x\) button, then enter \(-3.49\).
03

Obtain the result

After entering the expression, press the 'equals' button (usually denoted as \(=\)) to get the result. The calculator will display a number.
04

Round the result

Look at the number displayed and round it to four decimal places. If the fifth decimal place is 5 or more, round up the fourth decimal place by one. If it is less than 5, keep the fourth decimal place as is.

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

calculator usage
Using a calculator effectively is crucial for solving mathematical expressions like exponential functions. To solve for \( e^{-3.49}\), ensure your calculator is in scientific or standard mode. Here are the steps:
  • Turn on your calculator.
  • Find the \( e^x \) button, usually one of the main functions.
  • Input \(-3.49 \) after pressing the \( e^x \) button.
  • Press the equals button (\(=\)) to get the result.
This sequence of actions will give you the exponentiated value of \( e^{-3.49} \). It's simple once you become familiar with your calculator's layout.
rounding decimals
Rounding decimals is essential for achieving precision. After obtaining the result from your calculator, you need to round it to four decimal places. For instance, if your calculator shows the result as \(0.030197383\), follow these steps:
  • Look at the fifth decimal place (7 in this case). If it's 5 or greater, round the fourth decimal place up by one.
  • If the fifth decimal place is less than 5, keep the fourth decimal place as is.
  • In this example, since 7 is greater than 5, you round \(0.030197383\) to \(0.0302\).
This ensures that your results are accurate and meet the required precision.
scientific notation
Scientific notation is a way of expressing very large or very small numbers more compactly. Exponential functions often result in such numbers. For example, if your calculator gives you \(0.0302\), it is already in a simplified form. But for larger values, scientific notation would be useful.
  • For numbers like \(120000\), use \(1.2 \times 10^5\).
  • For small numbers like \(0.00034\), use \(3.4 \times 10^{-4}\).
This notation makes it easier to read, write, and understand complex numbers without dealing with numerous zeros.

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

Solve Explain why a logarithm base must be positive.

Solve. If no solution exists, state this. $$ 3^{3 x} \cdot 3^{x^{2}}=81 $$

For each function given below, (a) determine the domain and the range, (b) set an appropriate window, and (c) draw the graph. Graphs may vary, depending on the scale used. $$ f(x)=2 x^{3} \ln x $$

The concentration of acetaminophen in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 11 micrograms \(/\) milliliter \((\mathrm{mcg} / \mathrm{mL})\) of the drug in their blood plasma 1 hr after a 1000 -mg dosage and 2 micrograms / milliliter 6 hr after dosage. Data: tylenolprofessional.com; Mark Knopp, M.D. a) Find the value \(k,\) and write an equation for an exponential function that can be used to predict the concentration of acetaminophen, in micrograms / milliliter, t hours after a 1000 -mg dosage. b) Estimate the concentration of acetaminophen 3 hr after a 1000 -mg dosage. c) To relieve a fever, the concentration of acetaminophen should go no lower than \(4 \mathrm{mcg} / \mathrm{mL}\). After how many hours will a 1000 -mg dosage drop to that level? d) Find the half-life of acetaminophen.

Let \(c(w)\) represent the cost of mailing a package that weighs \(w\) pounds. Let \(f(n)\) represent the weight, in pounds, of \(n\) copies of a certain book. Explain what \((c \circ f)(n)\) represents.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.