Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN: 9781337111348
Author: Bruce Crauder, Benny Evans, Alan Noell
Publisher: Cengage Learning
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Chapter 6.3, Problem 7SBE

Estimating Rates of Change By direct calculation, estimate the value of d f d x for f ( x ) = 1 / x 2 at x = 4 . Use an increment of 0.0001 .

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A chemical processing plant must monitor a certain liquid substance in a batch of product they make. The substance is transferred from one tank into another in the manufacturing process and the rate of flow must be tracked. The function h(x) = 20(0.75)^x describes the height of the liquid in feet still remaining in the tank t minutes after the exit valve was tripped. a. Using the equation above, find the average rate of change in the height for the first 3 minutes. b. Estimate the instantaneous rate of change in the height at 5 minutes and illustrate this value on a graph. c. Interpret your answer to part b. within the context of the problem.

Chapter 6 Solutions

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Ch. 6.1 - Prob. 11ECh. 6.1 - Prob. 12ECh. 6.1 - Velocity What is the rate of change in directed...Ch. 6.1 - Sign of VelocityWhen directed distance is...Ch. 6.1 - Sign of VelocityWhen the graph of directed...Ch. 6.1 - Constant VelocityWhen velocity is constant, what...Ch. 6.1 - Constant Velocity When the graph of directed...Ch. 6.1 - Prob. 6SBECh. 6.1 - Prob. 7SBECh. 6.1 - Prob. 8SBECh. 6.1 - Prob. 9SBECh. 6.1 - Prob. 10SBECh. 6.1 - Change in Direction A graph of directed distance...Ch. 6.1 - Prob. 12SBECh. 6.2 - Prob. 1ECh. 6.2 - Reminder Round all answers to two decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Prob. 8ECh. 6.2 - Reminder Round all answers to decimal places...Ch. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - ReminderRound all answers to two decimal places...Ch. 6.2 - Reminder Round all answers to two decimal places...Ch. 6.2 - ReminderRound all answers to two decimal places...Ch. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - SKILL BUILDING EXERCISES Marginal Cost: Let C(n)...Ch. 6.2 - SKILL BUILDING EXERCISES Marginal Profit: Your...Ch. 6.2 - SKILL BUILDING EXERCISES Buying for the Short...Ch. 6.2 - SKILL BUILDING EXERCISES Buying a company: You are...Ch. 6.2 - Meaning Of Rate Change: What is the common term...Ch. 6.2 - A Mathematical Term: If f=f(x), then we use dfdx...Ch. 6.2 - Sign of the Derivative: Suppose f=f(x). What is...Ch. 6.2 - Prob. 8SBECh. 6.2 - Prob. 9SBECh. 6.2 - Prob. 10SBECh. 6.2 - Prob. 11SBECh. 6.2 - Prob. 12SBECh. 6.2 - Prob. 13SBECh. 6.2 - Prob. 14SBECh. 6.2 - Prob. 15SBECh. 6.2 - Prob. 16SBECh. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - Reminder Round all answers to two decimal places...Ch. 6.3 - Reminder Round all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Prob. 10ECh. 6.3 - ReminderRound all answers to two decimal places...Ch. 6.3 - Prob. 12ECh. 6.3 - Rate of Change for a Linear Function If f is the...Ch. 6.3 - Rate of Change for a Linear Function If f is the...Ch. 6.3 - Rate of Change from Data Suppose f=f(x) satisfies...Ch. 6.3 - Rate of Change from Data Suppose f=f(x) satisfies...Ch. 6.3 - Prob. 5SBECh. 6.3 - Prob. 6SBECh. 6.3 - Estimating Rates of Change By direct calculation,...Ch. 6.3 - Estimating Rates of Change with the CalculatorMake...Ch. 6.3 - Prob. 9SBECh. 6.3 - Prob. 10SBECh. 6.3 - Prob. 11SBECh. 6.3 - Prob. 12SBECh. 6.3 - Prob. 13SBECh. 6.3 - Prob. 14SBECh. 6.4 - ReminderRound all answers to two decimal places...Ch. 6.4 - Reminder Round all answers to two decimal places...Ch. 6.4 - Reminder Round all answers to two decimal places...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 1SBECh. 6.4 - Prob. 2SBECh. 6.4 - Prob. 3SBECh. 6.4 - New Equation of Change? The tax liability T in...Ch. 6.4 - Prob. 5SBECh. 6.4 - Prob. 6SBECh. 6.4 - Prob. 7SBECh. 6.4 - Prob. 8SBECh. 6.4 - Prob. 9SBECh. 6.4 - Prob. 10SBECh. 6.4 - A Leaky BalloonA balloon leaks air changes volume...Ch. 6.4 - Prob. 12SBECh. 6.4 - Solving an Equation of Change Solve the equation...Ch. 6.4 - Prob. 14SBECh. 6.4 - Filling a Tank The water level in a tank rises...Ch. 6.4 - Solving an Equation of Change Solve the equation...Ch. 6.5 - Reminder Round all answers to two decimal places...Ch. 6.5 - Prob. 2ECh. 6.5 - Prob. 3ECh. 6.5 - Prob. 4ECh. 6.5 - Prob. 5ECh. 6.5 - Prob. 6ECh. 6.5 - Prob. 7ECh. 6.5 - Prob. 8ECh. 6.5 - Prob. 9ECh. 6.5 - Prob. 10ECh. 6.5 - Prob. 11ECh. 6.5 - Prob. 12ECh. 6.5 - Prob. 13ECh. 6.5 - Prob. 1SBECh. 6.5 - Prob. 2SBECh. 6.5 - Prob. 3SBECh. 6.5 - Prob. 4SBECh. 6.5 - Prob. 5SBECh. 6.5 - Prob. 6SBECh. 6.5 - WaterWater flows into a tank, and a certain part...Ch. 6.5 - Prob. 8SBECh. 6.5 - Prob. 9SBECh. 6.5 - Prob. 10SBECh. 6.5 - Prob. 11SBECh. 6.5 - Prob. 12SBECh. 6.5 - Equation of ChangeFor the equation of change...Ch. 6.5 - Prob. 14SBECh. 6.CR - Prob. 1CRCh. 6.CR - Prob. 2CRCh. 6.CR - Prob. 3CRCh. 6.CR - Prob. 4CRCh. 6.CR - Prob. 5CRCh. 6.CR - Prob. 6CRCh. 6.CR - Prob. 7CRCh. 6.CR - Prob. 8CRCh. 6.CR - Prob. 9CRCh. 6.CR - Prob. 10CRCh. 6.CR - Prob. 11CRCh. 6.CR - Prob. 12CRCh. 6.CR - Prob. 13CRCh. 6.CR - Prob. 14CRCh. 6.CR - Prob. 15CRCh. 6.CR - Prob. 16CRCh. 6.CR - Prob. 17CRCh. 6.CR - Prob. 18CRCh. 6.CR - Reminder Round all answers to two decimal places...Ch. 6.CR - Prob. 20CR
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