To determine Description of at least one situation from the news or our life in which predictions must be made but a linear function is not a good model and brief discussion of the shape (on a graph) that we would expect the function to take Explanation Given: Describe at least one situation from the news or your own life in which predictions must be made but a linear function is not a good model. Briefly discuss the shape (on a graph) that you would expect the function to take. A function: A function describes how a dependent variable changes with respect to one or more independent variables. When there are two variables, we may denote their relationship as an ordered pair with the independent variable first: (independent variable, dependent variable). An exponential function of the form Q = Q 0 × ( 1 + r ) t (where t > 0 for growth and t < 0 for decay) to model the situation described by considering the following case of exponential growth and decay, “A certain drug breaks down in the human body at a rate of 15 % per hour. The initial amount of the drug in the bloodstream is 8 milligrams.” In an exponential function of the form Q = Q 0 × ( 1 + r ) t , for the given problem Q is the amount of drug in the blood stream at time t , Q 0 is the initial amount of drug in the blood stream, r is the rate of breakdown of drug, and t is the time period in hour. Thereby Q 0 = 8 mg, r = − 15 % = − 0.15 (as the drug in human body follows an exponential decay), Thereby Q = 8 × ( 1 − 0.15 ) t mg is the required exponential function for this problem. The variables in our function are amount of drug in the human body and the time in hour, where time in hour is the independent variable and amount of drug in the human body is the dependent variable. Q = 8 × ( 1 − 0.15 ) t mg is the required exponential function for this problem. Thereby the following table is obtained by calculating the amount of drug in the human body for time in hours from 1 to 10 Time t (in hours) Q = 8 × ( 1 − 0.15 ) t 1 8 ( 0.85 ) 1 = 8 ( 0.85 ) = 6.8 mg 2 8 ( 0.85 ) 2 = 8 ( 0.72 ) = 5.78 mg 3 8 ( 0.85 ) 3 = 8 ( 0.61 ) = 4.91 mg 4 8 ( 0.85 ) 4 = 8 ( 0.52 ) = 4.17 mg 5 8 ( 0.85 ) 5 = 8 ( 0.44 ) = 3.55 mg 6 8 ( 0...

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

6th Edition

ISBN: 9780321914620

Author: Jeffrey O. Bennett, William L. Briggs

Publisher: PEARSON

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Chapter 9.B, Problem 51E

To determine

Description of at least one situation from the news or our life in which predictions must be made but a linear function is not a good model and brief discussion of the shape (on a graph) that we would expect the function to take

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Chapter 9 Solutions

Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)

Ch. 9.A - Prob. 1QQ Ch. 9.A - Prob. 2QQ Ch. 9.A - Prob. 3QQ Ch. 9.A - Prob. 4QQ Ch. 9.A - 5. When you nuke a graph of the function \[z =...Ch. 9.A - 6. The values taken on by the dependent variable...Ch. 9.A - 7. Consider a function that describes how a...Ch. 9.A - Prob. 8QQ Ch. 9.A - Prob. 9QQ Ch. 9.A - 10. Suppose that two groups of scientists have...

Ch. 9.A - Prob. 1E Ch. 9.A - Prob. 2E Ch. 9.A - Prob. 3E Ch. 9.A - Prob. 4E Ch. 9.A - Prob. 5E Ch. 9.A - Prob. 6E Ch. 9.A - Prob. 7E Ch. 9.A - 8. My mathematical model fits the data perfectly,...Ch. 9.A - Coordinate Plane Review. Use the skills covered in...Ch. 9.A - 9-10: Coordinate Plane Review. Use the skills...Ch. 9.A - Identifying Functions. In each of the following...Ch. 9.A - Prob. 12E Ch. 9.A - Identifying Functions. In each of the following...Ch. 9.A - Identifying Functions. In each of the following...Ch. 9.A - Prob. 15E Ch. 9.A - Prob. 16E Ch. 9.A - Related Quantities. Write a short statement that...Ch. 9.A - Prob. 18E Ch. 9.A - Prob. 19E Ch. 9.A - Related Quantities. Write a short statement that...Ch. 9.A - Related Quantities. Write a short statement that...Ch. 9.A - 15-22: Related Quantities. Write a short statement...Ch. 9.A - 23. Pressure Function. Study Figure 9.6. Use the...Ch. 9.A - Prob. 24E Ch. 9.A - Prob. 25E Ch. 9.A - 25-26: Functions from Graphs. Consider the graphs...Ch. 9.A - Prob. 27E Ch. 9.A - 27-30: Functions from Data Tables. Each of the...Ch. 9.A - Prob. 29E Ch. 9.A - Prob. 30E Ch. 9.A - Prob. 31E Ch. 9.A - Prob. 32E Ch. 9.A - Rough Sketches of Functions. For each function,...Ch. 9.A - 31-42: Rough Sketches of Functions. For each...Ch. 9.A - Rough Sketches of Functions. For each function,...Ch. 9.A - Rough Sketches of Functions. For each function,...Ch. 9.A - Rough Sketches of Functions. For each function,...Ch. 9.A - Rough Sketches of Functions. For each function,...Ch. 9.A - Prob. 39E Ch. 9.A - Prob. 40E Ch. 9.A - Rough Sketches of Functions. For each function,...Ch. 9.A - Prob. 42E Ch. 9.A - Everyday Models. Describe three different models...Ch. 9.A - 44. Functions and Variables in the News. Identity...Ch. 9.A - Prob. 45E Ch. 9.A - 46. Variable Tables. Find data on the Web (or two...Ch. 9.B - A linear function is characterized by an...Ch. 9.B - You have a graph of a linear function. To...Ch. 9.B - The graph of a linear function is sloping downward...Ch. 9.B - Suppose that Figure 9. 11 is an accurate...Ch. 9.B - Which town would have the steepest slope on a...Ch. 9.B - Consider the function price = $100 - ( $3/yr) ×...Ch. 9.B - Consider the demand function given in Example 6,...Ch. 9.B - A line intersects the y-axis at a value of y = 7...Ch. 9.B - Consider a line with equation \[y = 12x - 3\]....Ch. 9.B - Charlie picks apples in the orchard at a constant...Ch. 9.B - What does it mean to say that a function is...Ch. 9.B - Prob. 2E Ch. 9.B - How is the rate of change of a linear function...Ch. 9.B - 4. How do you find the change in the dependent...Ch. 9.B - 3. Describe the general equation for a linear...Ch. 9.B - Prob. 6E Ch. 9.B - When I graphed the linear function, it turned out...Ch. 9.B - I graphed two linear functions, and the one with...Ch. 9.B - My freeway speed is the rate of change in my...Ch. 9.B - It's possible to make a linear model from any two...Ch. 9.B - Linear Functions. Consider the following graphs....Ch. 9.B - 11-16: Linear Functions. Consider the following...Ch. 9.B - 11-16: Linear Functions. Consider the following...Ch. 9.B - Linear Functions. Consider the following graphs a....Ch. 9.B - 11-16: Linear Functions. Consider the following...Ch. 9.B - 11-16: Linear Functions. Consider the following...Ch. 9.B - 17-22: Rate of Change Rule. The following...Ch. 9.B - Prob. 18E Ch. 9.B - 17-22: Rate of Change Rule. The following...Ch. 9.B - Prob. 20E Ch. 9.B - Prob. 21E Ch. 9.B - Prob. 22E Ch. 9.B - 23-20: Linear Equations. The following situations...Ch. 9.B - Prob. 24E Ch. 9.B - 23-20: Linear Equations. The following situations...Ch. 9.B - Prob. 26E Ch. 9.B - 23-28: Linear Equations. The following situations...Ch. 9.B - Prob. 28E Ch. 9.B - Prob. 29E Ch. 9.B - Prob. 30E Ch. 9.B - 29-34: Equations from Two Data Points. Create the...Ch. 9.B - Equations from Two Data Points. Create the...Ch. 9.B - Prob. 33E Ch. 9.B - Prob. 34E Ch. 9.B - Prob. 35E Ch. 9.B - Prob. 36E Ch. 9.B - Prob. 37E Ch. 9.B - Prob. 38E Ch. 9.B - Prob. 39E Ch. 9.B - 35-42: Algebraic Linear Equations. For the...Ch. 9.B - 35-42: Algebraic Linear Equations. For the...Ch. 9.B - Algebraic Linear Equations. For the following...Ch. 9.B - Linear Graphs. The following situations can be...Ch. 9.B - Prob. 44E Ch. 9.B - Linear Graphs. The following situations can be...Ch. 9.B - Prob. 46E Ch. 9.B - Prob. 47E Ch. 9.B - Prob. 48E Ch. 9.B - Wildlife Management. A common technique for...Ch. 9.B - Linear Models. Describe at least two situations...Ch. 9.B - 51. Nonlinear Models. Describe at least one...Ch. 9.B - Alcohol Metabolism. Most drugs are eliminated from...Ch. 9.B - Properly Depreciation. Go to the IRS website, and...Ch. 9.C - Which statement is true about exponential growth?...Ch. 9.C - A city's population starts at 100,000 people and...Ch. 9.C - A city’s population suns at 100,000 people and...Ch. 9.C - Prob. 4QQ Ch. 9.C - Prob. 5QQ Ch. 9.C - Figure 9.18(b) shows the graph of an exponentially...Ch. 9.C - Polly received a large dose of an antibiotic and...Ch. 9.C - The half-life of carbon-14 is 5700 years, and...Ch. 9.C - Prob. 9QQ Ch. 9.C - Compare the list two forms of the exponential...Ch. 9.C - Prob. 1E Ch. 9.C - Prob. 2E Ch. 9.C - 3. Describe how you tan graph an exponential...Ch. 9.C - 4. Describe the meaning of each of the three forms...Ch. 9.C - Prob. 5E Ch. 9.C - Prob. 6E Ch. 9.C - After 100 years, a population growing at a rate of...Ch. 9.C - When 1 used the exponential function in model the...Ch. 9.C - We can use the hurt that radioactive materials...Ch. 9.C - I used the exponential function to figure how much...Ch. 9.C - Review of logarithms. Use the skills coveted in...Ch. 9.C - Prob. 12E Ch. 9.C - Prob. 13E Ch. 9.C - Prob. 14E Ch. 9.C - Review of logarithms. Use the skills coveted in...Ch. 9.C - 11-26: Review of logarithms. Use the skills...Ch. 9.C - 11-26: Review of logarithms. Use the skills...Ch. 9.C - 11-26: Review of logarithms. Use the skills...Ch. 9.C - Review of logarithms. Use the skills coveted in...Ch. 9.C - Prob. 20E Ch. 9.C - Prob. 21E Ch. 9.C - Prob. 22E Ch. 9.C - Prob. 23E Ch. 9.C - Prob. 24E Ch. 9.C - Prob. 25E Ch. 9.C - Prob. 26E Ch. 9.C - 27-34. Exponential growth and decay laws. Consider...Ch. 9.C - Prob. 28E Ch. 9.C - . Exponential growth and decay laws. Consider the...Ch. 9.C - . Exponential growth and decay laws. Consider the...Ch. 9.C - . Exponential growth and decay laws. Consider the...Ch. 9.C - Prob. 32E Ch. 9.C - Prob. 33E Ch. 9.C - . Exponential growth and decay laws. Consider the...Ch. 9.C - Prob. 35E Ch. 9.C - Annual vs. Monthly Inflation. Answer the following...Ch. 9.C - Hyperinflation in Germany. In 1923, Germany...Ch. 9.C - Prob. 38E Ch. 9.C - 39. Extinction by Poaching. Suppose that poaching...Ch. 9.C - World Oil Production. Annual world oil production...Ch. 9.C - Prob. 41E Ch. 9.C - Aspirin Metabolism. Assume that for the average...Ch. 9.C - Prob. 43E Ch. 9.C - Prob. 44E Ch. 9.C - Prob. 45E Ch. 9.C - Metropolitan Population Growth. A small city had a...Ch. 9.C - Rising Costs. Between 2005 and 2010, the average...Ch. 9.C - Periodic Drug Doses. It is common to take a drug...Ch. 9.C - Increasing Atmospheric Carbon Dioxide. Between...Ch. 9.C - Prob. 50E Ch. 9.C - Inflation Rate in the News. Find a news report...Ch. 9.C - Prob. 52E Ch. 9.C - Radiometric Dating in the News. Find a news report...Ch. 9.C - Prob. 54E Ch. 9.C - Prob. 55E

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