amos 94 CHAPTER 2 LIMITS AND DERIVATIVES 2.1 Exercises 1. A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) 5 10 15 25 20 30 V (gal) 694 28 0 444 250 111 (a) If P is the point (15, 230) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t 5, 10, 20 25, and 30. sdi b 01 (b) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines. (c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.) 0 A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t min- tes. When the data in the table are graphed, the slope of the angent line represents the heart rate in beats per minute. 01 t 1909

amos 94 CHAPTER 2 LIMITS AND DERIVATIVES 2.1 Exercises 1. A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. t (min) 5 10 15 25 20 30 V (gal) 694 28 0 444 250 111 (a) If P is the point (15, 230) on the graph of V, find the slopes of the secant lines PQ when Q is the point on the graph with t 5, 10, 20 25, and 30. sdi b 01 (b) Estimate the slope of the tangent line at P by averaging the slopes of two secant lines. (c) Use a graph of the function to estimate the slope of the tangent line at P. (This slope represents the rate at which the water is flowing from the tank after 15 minutes.) 0 A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t min- tes. When the data in the table are graphed, the slope of the angent line represents the heart rate in beats per minute. 01 t 1909

Name: I don't know understand one and it's parts. amos94CHAPTER 2 LIMITS AND
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: I don't know understand one and it's parts. amos94CHAPTER 2 LIMITS AND DERIVATIVES2.1 Exercises1. A tank holds 1000 gallons of water, which drains from thebottom of the tank in half an hour. The values in the table showthe volume V of water remaining

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

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.6: Optimization

Problem 10E: Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per...

See similar textbooks

Similar questions

Minimum Find the minimum value of x2+20/(x+1) on the horizontal span of 0 to 10.
Finding a Minimum Suppose the function f=x392x2+6x+1 describes a physical situation that makes sense only for whole numbers between 1 and 5. For what value of x does f reach a minimum and what is that minimum value?
Sales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the product as a function of the sales level s, in thousands of dollars. The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s, and the unattained sales. Assume that the constant of proportionality is 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?
Water Flea F. E Smith has reported on population growth of the water flea. In one experiment, he found that the time t, in days, required to reach a population of N is given by the relation e0.44t=NN0(228N0228N)4.46. Here N0 is the initial population size. If the initial population size is 50, how long is required for the population to grow to 125?