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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
The logistic growth functionmodels the percentage, P(x), of Americans who are x years old with some coronary heart disease. Use the function to solve Exercises 43–46.At what age is the percentage
Exercises 47–52 present data in the form of tables. For each data set shown by the table,a. Create a scatter plot for the data.b. Use the scatter plot to determine whether an exponential function,
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 47–52, the graph of a logarithmic function is given. Select the function for each graph from the following options: f(x) = log3 x, g(x) = F(x) = −log3 x, G(x) log3(x - 1), h(x) - 1),
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 47–52, graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn
On the Richter scale, the magnitude, R, of an earthquake of intensity I is given by R = log I /I0 , where I0 is the intensity of a barely felt zero-level earthquake. If the intensity of an
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
Use the compound interest formulas and A = Pert to solve Exercises 53–56. Round answers to the nearest cent.Suppose that you have $12,000 to invest. Which investment yields the greater return over
Use the compound interest formulas and A = Pert to solve Exercises 53–56. Round answers to the nearest cent.Find the accumulated value of an investment of $10,000 for 5 years at an interest rate of
In Exercises 53–58, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each
In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.logb 7 + logb 3
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 53–56, rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places.y = 1000(7.3)x
In Exercises 53–58, begin by graphing f(x) = log2 x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each
Use the compound interest formulas and A = Pert to solve Exercises 53–56. Round answers to the nearest cent.Find the accumulated value of an investment of $5000 for 10 years at an interest rate of
Use the exponential decay model, A = A0ekt, to solve Exercises 28–31. Round answers to one decimal place.The half-life of thorium-229 is 7340 years. How long will it take for a sample of this
The logistic growth functiondescribes the population, f(t), of an endangered species of elk t years after they were introduced to a nonthreatening habitat.a. How many elk were initially introduced to
In Exercises 25–34, begin by graphing f(x) = 2x. Then use transformations of this graph to graph the given function. Be sure to graph and give equations of the asymptotes. Use the graphs to
In Exercises 21–42, evaluate each expression without using a calculator. log, V7
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason.log3(log8 8)
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 53–56, rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places.y = 2.5(0.7)x
In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1.log 3 - 3 log x
The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine
In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
Describe the shape of a scatter plot that suggests modeling the data with an exponential function.
In Exercises 61–64, give the equation of each exponential function whose graph is shown. y = 0 -1 y -2- -4- -6- ~8- -10- (0, -1) (1,te) X (2, -e²)
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
You take up weightlifting and record the maximum number of pounds you can lift at the end of each week. You start off with rapid growth in terms of the weight you can lift from week to week, but then
The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 61–64, give the equation of each exponential function whose graph is shown. (-2, e²) (-1, e): -2 -1 y 10- 9- ·8- 7- -6+ --5- 4- [(0,1) 2 y = 0 X
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
Use a calculator with a yx key or a ∧ key to solve Exercises 65–70.India is currently one of the world’s fastest-growing countries. By 2040, the population of India will be larger than the
In Example 1, we used two data points and an exponential function to model the population of the United States from 1970 through 2010. The data are shown again in the table. Use all five data points
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Example 1, we used two data points and an exponential function to model the population of the United States from 1970 through 2010. The data are shown again in the table. Use all five data points
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Example 1, we used two data points and an exponential function to model the population of the United States from 1970 through 2010. The data are shown again in the table. Use all five data points
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
Use a calculator with a yx key or a ∧ key to solve Exercises 65–70.The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
Use a calculator with a yx key or a ∧ key to solve Exercises 65–70.The formula S = C(1 + r)t models inflation, where C = the value today, r = the annual inflation rate, and S = the inflated value
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Example 1, we used two data points and an exponential function to model the population of the United States from 1970 through 2010. The data are shown again in the table. Use all five data points
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
Use a calculator with a yx key or a ∧ key to solve Exercises 65–70.The formula S = C(1 + r)t models inflation, where C = the value today, r = the annual inflation rate, and S = the inflated value
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
Use a calculator with a yx key or a ∧ key to solve Exercises 65–70.A decimal approximation for √3 is 1.7320508. Use a calculator to find 21.7, 21.73, 21.732, 21.73205, and 21.7320508. Now find
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
Use a calculator with a yx key or a ∧ key to solve Exercises 65–70.A decimal approximation for π is 3.141593. Use a calculator to find 23, 23.1, 23.14, 23.141, 23.1415, 23.14159, and 23.141593.
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
The figure shows the number of people in the United States age 65 and over, with projected figures for the year 2020 and beyond.a. Let x represent the number of years after 1899 and let y represent
In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log5 13
Use a calculator with an ex key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log6 17
Use a calculator with an ex key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation,
In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log14 87.5
Use a calculator with an ex key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
In Exercises 71–78, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places.log16 57.2
In Exercises 74–79, solve each logarithmic equation.log4(3x - 5) = 3
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary,
In Exercises 73–76, determine whether each statement makes sense or does not make sense, and explain your reasoning.I used an exponential model with a positive growth rate to describe the
Use a calculator with an ex key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through
The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each
Use a calculator with an ex key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through
Use a calculator with an ex key to solve Exercises 71–76. The bar graph shows the percentage of U.S. high school seniors who applied to more than three colleges for selected years from 1980 through

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