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mathematics
college algebra graphs and models

Questions and Answers of College Algebra Graphs And Models

What is a rational inequality?
In Exercises 98–99, use a graphing utility to graph f and g in the same viewing rectangle. Then use the Zoom out feature to show that f and g have identical end behavior.f(x) = x3 - 6x + 1, g(x) =
If f is a polynomial or rational function, explain how the graph of f can be used to visualize the solution set of the inequality f(x) < 0.
Find the average rate of change of f(x) = 2x from x1 = 4 to x2 = 9.
Use a graphing utility to graph y = 1/x , y = 1/x3, and 1/x5 in the same viewing rectangle. For odd values of n, how does changing n affect the graph of y = 1/xn?
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places.e2.3
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.32x = 8
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs
In Exercises 9–14, complete the table. Round projected populations to one decimal place and values of k to four decimal places. Country Philippines 2010 Population (millions) 99.9 Projected
In Exercises 23–25, write each expression as a single logarithm. 8 log7x 1 1 log, y 3
In Exercises 21–26, complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Radium-226 Half-Life 1620 years Decay Rate, k
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logs Vx 25
In Exercises 21–22, expand and evaluate numerical terms. In(e¹9x20)
In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3*, g(x) = 3x-1, h(x) = 3x - 1, F(x) = -3*, G(x) = 3*, H(x)
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 √x 64
Use the compound interest formulas to solve Exercises 23–25.How long, to the nearest tenth of a year, will it take $4000 to grow to $8000 at 5% annual interest compounded quarterly?
In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3*, g(x) = 3x-1, h(x) = 3x - 1, F(x) = -3*, G(x) = 3*, H(x)
In Exercises 21–26, complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Krypton-85 Half-Life Decay Rate, k 6.3% per year = -0.063
In Exercises 21–42, evaluate each expression without using a calculator.log2 64
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. ex+4 = 1 e2x e
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 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb(xy³)
In Exercises 21–26, complete the table. Round half-lives to one decimal place and values of k to six decimal places. Radioactive Substance Tritium Half-Life Decay Rate, k 5.5% per year = -0.055
In Exercises 21–22, expand and evaluate numerical terms. log √xy 1000
Use the compound interest formulas to solve Exercises 23-25.Suppose you have $3000 to invest. Which investment yields the greater return over 10 years: 6.5% compounded semiannually or 6% compounded
In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3*, g(x) = 3x-1, h(x) = 3x - 1, F(x) = -3*, G(x) = 3*, H(x)
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason.log16 4
In Exercises 21–42, evaluate each expression without using a calculator.log7 49
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. ex+1 || 1 e
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log5 25
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb(x²y)
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. logㅠㅠ ㅠ
In Exercises 9–20, write each equation in its equivalent logarithmic form. 8 = 300
In Exercises 20–22, simplify each expression.log6 1
In Exercises 21–42, evaluate each expression without using a calculator.log4 16
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason.log3(-9)
In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3*, g(x) = 3x-1, h(x) = 3x - 1, F(x) = -3*, G(x) = 3*, H(x)
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. InVx
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log100 0.1
Use the exponential decay model for carbon-14, A = A0e-0.000121t, to solve Exercises 19–20.Skeletons were found at a construction site in San Francisco in 1989. The skeletons contained 88% of the
In Exercises 20–22, simplify each expression.logb b
You are paid time-and-a-half for each hour worked over 40 hours a week. Last week you worked 50 hours and earned $660. What is your normal hourly salary?
In Exercises 9–20, write each equation in its equivalent logarithmic form. 7 = 200
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.81-x = 4x+2
In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 3*, g(x) = 3x-1, h(x) = 3x - 1, F(x) = -3*, G(x) = 3*, H(x)
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. In Vx
On the decibel scale, the loudness of a sound, D, in decibels, is given by is the intensity of the sound, in watts per meter2, and I0 is the intensity of a sound barely audible to the human ear. If
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. 10log 13
Use the exponential decay model for carbon-14, A = A0e-0.000121t, to solve Exercises 19–20.Prehistoric cave paintings were discovered in a cave in France. The paint contained 15% of the original
A baseball player hits a pop fly into the air. The function s(t) = -16t2 + 64t + 5 models the ball’s height above the ground, s(t), in feet, t seconds after it is hit. Use the function to solve
In Exercises 20–22, simplify each expression.ln e5x
In Exercises 9–20, write each equation in its equivalent logarithmic form. Ꮟ3 ; = 343
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 9x: 1 3/3
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents.8x+3 = 16x-1
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.8)*
In Exercises 19–29, evaluate each expression without using a calculator. If evaluation is not possible, state the reason.log4 64
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. In evi
The half-life of the radioactive element plutonium-239 is 25,000 years. If 16 grams of plutonium-239 are initially present, how many grams are present after 25,000 years? 50,000 years? 75,000 years?
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log M-8
A baseball player hits a pop fly into the air. The function s(t) = -16t2 + 64t + 5 models the ball’s height above the ground, s(t), in feet, t seconds after it is hit. Use the function to solve
In Exercises 9–20, write each equation in its equivalent logarithmic form. b3 : = 1000
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 4x = 1 V2
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. x(90) = (x)f
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log6 5
In Exercises 16–18, write each equation in its equivalent logarithmic form.13y = 874
You discover that the number of hours you sleep each night varies inversely as the square of the number of cups of coffee consumed during the early evening. If 2 cups of coffee are consumed, you get
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N-6
In Exercises 11–18, solve each equation.ln(x - 4) - ln(x + 1) = ln 6
The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds? 30 seconds? 40 seconds? 50
In Exercises 9–20, write each equation in its equivalent logarithmic form. 152 = = X
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. LA = 9 7 x-2
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (¹)*
In Exercises 16–18, write each equation in its equivalent logarithmic form.b4 = 625
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 7 logox¹
In Exercises 9–20, write each equation in its equivalent logarithmic form. 13² = x
In Exercises 11–18, solve each equation.log x + log(x + 15) = 2
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log3 (log2)
In Exercises 13–15, write each equation in its equivalent exponential form. log3 81 = y
An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e-0.000121t describes the amount of carbon-14 present after t years. Use this model to solve Exercises 15–16.How many
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. x-3 4 9 9A=
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. h(x) = (¹) *
In Exercises 16–18, write each equation in its equivalent logarithmic form.63 = 216
In Exercises 9–20, write each equation in its equivalent logarithmic form. √64=4
In Exercises 11–18, solve each equation.2 ln(3x) = 8
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log₂(log3 81)
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. X 413 || (x)8
An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e-0.000121t describes the amount of carbon-14 present after t years. Use this model to solve Exercises 15–16.How many
In Exercises 9–14, complete the table. Round projected populations to one decimal place and values of k to four decimal places. Country Bulgaria 2010 Population (millions) 7.1 Projected 2050
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log, x³
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 52-x = 1 125
Write the point-slope form and the slope-intercept form of the line passing through (1, 3) and (3, -3).
In Exercises 13–15, write each equation in its equivalent exponential form. 3= log4 x
In Exercises 9–14, complete the table. Round projected populations to one decimal place and values of k to four decimal places. Country Germany 2010 Population (millions) 82.3 Projected 2050
In Exercises 11–18, solve each equation.log6(4x - 1) = 3
In Exercises 10–20, evaluate each expression without using a calculator. If evaluation is not possible, state the reason. log3 1
Fill in each blank so that the resulting statement is true.The logarithmic function with base e is called the_________ logarithmic function. The function f(x) = loge x is usually expressed as
In Exercises 9–14, complete the table. Round projected populations to one decimal place and values of k to four decimal places. Country Madagascar 2010 Population (millions) 21.3 Projected 2050
A cup of coffee is taken out of a microwave oven and placed in a room. The temperature, T, in degrees Fahrenheit, of the coffee after t minutes is modeled by the function T = 70 + 130e-0.04855t. The
In Exercises 13–15, write each equation in its equivalent exponential form. -IN = log49 7

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