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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.ex4 = 1000
Determine whether each function graphed or defined is one-to-one.y = 3x3 - 6
Write an equivalent statement in logarithmic form.ab = c
Solve each equation. 27 = 3 log, 64
How long will it take any quantity of iodine-131 to decay to 25% of its initial amount, knowing that it decays according to the exponential function A(t) = A0 e-0.087t, where t is time in days?
Find each value. If applicable, give an approximation to four decimal places. 518 log 342
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed. 3 2,
Write each equation in exponential form.log 1000 = 3
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.ex2 = 100
Determine whether each function graphed or defined is one-to-one.y = 2x3 - 1
Write an equivalent statement in logarithmic form. -3 = 1000 10
Solve each equation. = 5 32 log,
If 1 g of strontium-90 is present initially, and 2 yr later 0.95 g remains, how much strontium-90 will be present after 5 yr?
Find the domain of each function. Write answers using interval notation. f(x) = х3 — 8
Find each value. If applicable, give an approximation to four decimal places.log (296 × 12)
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed. 5 2
Write each equation in logarithmic form.Graph ƒ(x) = (1/5)x + 2 - 1. Give the domain and range.
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.3x-4 = 72x+5
Determine whether each function graphed or defined is one-to-one. y = -V100 – x2
For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so. f(x)=x-9, x3
Solve each equation. x = log3 81
If 12 g of a radioactive substance are present initially and 4 yr later only 6.0 g remain, how much of the substance will be present after 7 yr?
Find the domain of each function. Write answers using interval notation. -1 f(x) = x³ – 1
Find each value. If applicable, give an approximation to four decimal places.log (387 × 23)
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.
Write each equation in logarithmic form. 413
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.6x+1 = 42x-1
Determine whether each function graphed or defined is one-to-one. у%3D V36 — х?
For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so. |f(x) = V5 – x+
Solve each equation. x = logs 625
Find the half-life of tritium, a radioactive isotope of hydrogen, which decays according to the function A(t) = A0 e -0.056t, where t is time in years.
Find the domain of each function. Write answers using interval notation. х3 — 1 f(x) : x2 – 1
Find each value. If applicable, give an approximation to four decimal places.log 0.0055
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.g(-3)
Write each equation in logarithmic form.1001/2 = 10
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.2x+3 = 52x
Determine whether each function graphed or defined is one-to-one.y = 4x + 20
For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so. 2х — 1 f(x) 5 — Зх
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. -3 log4 64
Find the half-life of radium-226, which decays according to the function A(t) = A0 e-0.00043t, where t is time in years.
Find the domain of each function. Write answers using interval notation. f(x) = e²+x+4
Find each value. If applicable, give an approximation to four decimal places.log 0.0022
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.g(-2)
Write each equation in logarithmic form.25 = 32
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.4x-1 = 32x
Determine whether each function graphed or defined is one-to-one.y = 2x - 8
For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so.ƒ(x) = 3x2
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. log a 81 = 8
Repeat Exercise 15 for 500 g of plutonium-241, which decays according to the function A(t) = A0 e-0.053t, where t is time in years.Exercise 15(a) 4 yr, (b) 8 yr, (c) 20 yr. (d) Find the half-life.
Find the domain of each function. Write answers using interval notation. f(x) = In |x² – 5
Find each value. If applicable, give an approximation to four decimal places.log 94
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.g(3)
Match each equation with the figure that most closely resembles its graph.y = 0.3x D. A. C. B. х х
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.0.6x = 3
Determine whether each function graphed or defined is one-to-one. y
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form.log5 5 = 1
For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so.ƒ(x) = 2(x + 1)3
Solve each problem.A sample of 500 g of radioactive lead-210 decays to polonium-210 according to the function A(t) = 500e-0.032t, where t is time in years. Find the amount of radioactive lead remaining after,(a) 4 yr, (b) 8 yr, (c) 20 yr. (d) Find the half-life.
Find the domain of each function. Write answers using interval notation. f(x) = Vx³ – 1|
Find each value. If applicable, give an approximation to four decimal places.log 63
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.g(2)
Match each equation with the figure that most closely resembles its graph.y = ln x D. A. C. B. х х
Determine whether each function graphed or defined is one-to-one.
For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both ƒ and ƒ-1. If the function is not one-to-one, say so.ƒ(x) = 3x - 6
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.0.8x = 4
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form.log6 36 = 2
An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0 ekt that models the situation, give the exact value of k in terms of natural logarithms.y0 = 8.1 kg; After 4 yr,
Find the domain of each function. Write answers using interval notation. x2 – 25 f(x) x + 5
Find each value. If applicable, give an approximation to four decimal places.log 0.01
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.ƒ(-3)
Match each equation with the figure that most closely resembles its graph.y = ex D. A. C. B. х х
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form. 3
Determine whether each function graphed or defined is one-to-one. х
Determine the inverse of the function ƒ(x) = log5 x.
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form.10-4 = 0.0001
An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0 ekt that models the situation, give the exact value of k in terms of natural logarithms.y0 = 2.4 lb; After 2 yr,
Find the domain of each function. Write answers using interval notation. f(x) 2x2 х+7
Find each value. If applicable, give an approximation to four decimal places.log 0.1
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.ƒ(-2)
Match each equation with the figure that most closely resembles its graph.y = log0.3 x D. A. C. B. х х
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.
Determine whether each function graphed or defined is one-to-one. y
The functions in Exercises 9–12 form two pairs of inverse functions. Determine which functions are inverses of each other.Exercises 9–12y = log3 (x + 2)y = 5 - 2xy = log2 (5 - x)y = 3x - 2 A. B. C. D.
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. -3 27 3 00
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form.25 = 32
An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0 ekt that models the situation, give the exact value of k in terms of natural logarithms.y0 = 20 mg; The half-life
Find the domain of each function. Write answers using interval notation.ƒ(x) = 21/x
Find each value. If applicable, give an approximation to four decimal places.log 107
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.ƒ(3)
Work each problem.True or false? The x-coordinate of the x-intercept of the graph of y = ƒ(x) is the y-coordinate of the y-intercept of the graph of y = ƒ-1(x).
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.5x = 13
Determine whether each function graphed or defined is one-to-one. y х
If ƒ(x) = 4x, what is the value of ƒ(log4 12)?
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form.34 = 81
An initial amount of a radioactive substance y0 is given, along with information about the amount remaining after a given time t in appropriate units. For an equation of the form y = y0 ekt that models the situation, give the exact value of k in terms of natural logarithms.y0 = 10 mg; The half-life
Find the domain of each function. Write answers using interval notation. f(x) = Vx² – 7x – 8
Find each value. If applicable, give an approximation to four decimal places.log 1012
For ƒ(x) = 3x and g(x) = [1/4]x, find each of the following. Round answers to the nearest thousandth as needed.ƒ(2)
Work each problem.To have an inverse, a function must be a(n) ____________ function.
Solve each equation. In Exercises, give irrational solutions as decimals correct to the nearest thousandth. In Exercises, give solutions in exact form.3x = 7
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