Water in a Tank The graph shows the amount ofwater in a 100-gallon tank after x minutes have elapsed.100908070605040302010012345678 9 10Time (minutes)(a) Is water entering or leaving the tank? How muchwater is in the tank after 3 minutes?(b) Find both the x- and y-intercepts. Interpret eachintercept.(c) Find the slope-intercept form of the equationof the line. Interpret the slope.(d) Use the graph to estimate the x-coordinate of thepoint (x, 50) that lies on the line.Water(gallons)

Graph of the water tank at time t is given, we have to find the required values

Answered: Water in a Tank The graph shows the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 64E

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Population The population y (in thousands) of Raleigh, North Carolina, from 2000 to 2014 can be approximated by the model y=11.09t+293.4,0t14, where t represents the year, with t=0 corresponding to 2000 (see figure). (a) Graphically estimate the y-intercept of the graph. (b) Find algebraically and interpret the y-intercept of the graph. (c) Use the model to predict the year in which the population will be 538,000. Does your answer seem reasonable? Explain.
Population The population y (in thousands) of Buffalo, New York, from 2000 to 2014 can be approximated by the model y=2.60t+291.7,0t14, where t represents the year, with t=0 corresponding to 2000 (see figure). (a) Graphically estimate the y-intercept of the graph. (b) Find algebraically and interpret the y-intercept of the graph. (c) Use the model to predict the year in which the population will be 239,000. Does your answer seem reasonable? Explain.
Find the slope of the line shown in the graph.
Geometry The length and width of a rectangular garden are 15 meters and 10 meters, respectively. A walkway of width x surrounds the garden. (a) Draw a diagram that gives a visual representation of the problem. (b) Write the equation for the perimeter y of the walkway in terms of x. (c) Use a graphing utility to graph the equation for the perimeter. (d) Determine the slope of the graph in part (c). For each additional one-meter increase in the width of the walkway, determine the increase in its perimeter.
Lidocaine Lidocaine is a drug used to treat irregular heartbeats. After an injection of a 100-mg dose of lidocaine, the amount of the drug in a patients bloodstream is 33.67(e0.0075731te0.12043t)mg at time t minutes after the injection. a. Make a graph of the amount of drug in the bloodstream for t up to 4 hours 240 minutes. b. When does the drug reach its maximum level in the bloodstream? c. For a person of typical size, the drug is effective as long as the amount in the bloodstream is at least 7.5 mg. For how long is the drug at or above that level? Hint: The drug is at that level twice. d. For a person of typical size, the lethal level occurs when the amount in the bloodstream exceeds 30 mg. Is this dose lethal for such a person? e. For a small person, the lethal level occurs when the amount in the bloodstream exceeds 15 mg. Is this dose lethal for such a person? If so, after how many minutes will it be lethal?
Buying a Car: If you buy a 25,000 car at an APR of 6, then your monthly payments depends on the term of the loan. If the term is t months, then your monthly payment is M=25,0000.0051.005t1.005t1dollars a. Make a graph of the monthly payments versus the length of the term, in months. Include terms from 12 to 60 months. b. Is the graph increasing or decreasing? What does that mean in practical terms? c. Do you lower your monthly payment more by changing the term of the loan from 12 to 24 months or from 48 to 60 months? Suggestion: you dont need a calculation here. The concavity of the graph can give you the answer.
Filling a Pond A large koi pond is filled from a garden hose at the rate of 10 gal/min. Initially, the pond contains 300 gal of water. a Find a linear function V that models the volume of water in the pond at any time t. b If the pond has a capacity of 1300 gal, how long does it take to completely fill the pond?
Temperature An object at a temperature of 160C was removed from a furnace and placed in a room at 20C. The temperature T of the object was measured each hour h and recorded in the table. A model for the data is T=20+140e0.68h (a)The figure below shows the graph of the model. Use the graph to identify the horizontal asymptote of the model and interpret the asymptote in the context of the problem. (b) Use the model to approximate the time it took for the object to reach a temperature of 100C.
Temperature An object at a temperature of 160C was removed from a furnace and placed in a room at 20C. The temperature T of the object was measured each hour h and recorded in the table. A model for the data is T=20+140e0.68h. (a) The figure below shows the graph of the model. Use the graph to identify the horizontal asymptote of the model and interpret the asymptote in the context of the problem. (b) Use the model to approximate the time it took for the object to reach a temperature of 100C.
Fluid Flow The intake pipe of a 100-gallon tank has a flow rate of 10 gallons per minute, and two drainpipes have flow rates of 5 gallons per minute each. The figure shows the volume V of fluid in the tank as a function of time t. Determine whether the input pipe and each drainpipe are open or closed in specific subintervals of the 1 hour of time shown in the graph. (There are many correct answers.)
Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0r70 Where y represents the life expectancy and t is the time in years, with t=0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. Verify your answer algebraically. (d) Identify the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explain
Population Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0t70 Where y represents the life expectancy and t is the time in years, with t = 0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain. (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. verify your answer algebraically. (d) Find the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now?

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