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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Determine whether each function graphed or defined is one-to-one. y х
Find the value of log3 40 to four decimal places.
Use the properties of logarithms to rewrite each expression. Assume all variables represent positive real numbers.3 log4 x - 5 log4 y
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 = 30 g; After 6 hr, 10
Find the domain of each function. Write answers using interval notation. x + 7 f(x) = log 3
The graph of y = ln x shows a point on the graph. Write the logarithmic equation associated with that point. (2.75, 1.0116009) 4 6 -1 y = In x 2.
Solve each equation. Round answers to the nearest hundredth as needed.10,000 = 5000(1 + r)25
Work each problem.The graphs of two functions are shown. Based on their graphs, are these functions inverses? E TADIAH H aAL PLOATUTA EH FAIH H 10 16.1 -16.1- -10
An exponential equation such as 5x = 9 can be solved for its exact solution using the meaning of logarithm and the change-of-base theorem. Because x is the exponent to which 5 must be raised in order to obtain 9, the exact solution isFor each equation, give the exact solution in three forms similar
Fill in the blank(s) to correctly complete each sentence.If ƒ(-4) = 16 and ƒ(4) = 16, then ƒ____________ have an inverse because. (does/does not)
Given logb 9 = 3.1699 and logb 5 = 2.3219, find the value of logb 225.
Use the properties of logarithms to rewrite each expression. Assume all variables represent positive real numbers. 2x log10
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 = 60 g; After 3 hr, 20
Find the domain of each function. Write answers using interval notation.ƒ(x) = log5(16 - x2)
Answer each of the following.The graph of y = log x shows a point on the graph. Write the logarithmic equation associated with that point. y (8, 0.90308999) + 4 y = log x -1
Solve each equation. Round answers to the nearest hundredth as needed. 0.03 8(4) 4 A = 2000 1 +
Work each problem.Suppose ƒ(t) is the amount an investment will grow to t years after 2004. What does ƒ-1($50,000) represent?
An exponential equation such as 5x = 9 can be solved for its exact solution using the meaning of logarithm and the change-of-base theorem. Because x is the exponent to which 5 must be raised in order to obtain 9, the exact solution isFor each equation, give the exact solution in three forms similar
Fill in the blank(s) to correctly complete each sentence.If a function ƒ has an inverse and ƒ(-3) = 6, then ƒ-1(6) = _________.
Assuming all variables represent positive real numbers, use properties of logarithms to rewrite Vx.y log3 рФ
In Exercises, match each function with its graph from choices A–D.y = 3x - 2 А. В. С. D.
In Exercises, match each function with its graph from choices A–D.y = log2 (5 - x) A. B. C. D.
In Exercises, match each function with its graph from choices A–D.y = 5 - 2x A. B. C. D.
In Exercises, match each function with its graph from choices A–D.y = log3 (x + 2) A. B. C. D.
Sketch the graph of each function. Give the domain and range.g(x) = log1/5 x
Strontium-90 decays according to the exponential function y = y0 e-0.0241t, where t is time in years. Match each question in Column I with the correct procedure in Column II to answer the question.How long will it take for any amount of Strontium-90 to decay to 75% of its initial amount? A. Solve
Find the domain of each function. Write answers using interval notation. f(x) = Vx³ + 7x – 4
Answer each of the following.Between what two consecutive integers must log2 12 lie?
Find the inverse of each function that is one-to-one. f(x) 3D V25 — х?
An exponential equation such as 5x = 9 can be solved for its exact solution using the meaning of logarithm and the change-of-base theorem. Because x is the exponent to which 5 must be raised in order to obtain 9, the exact solution isFor each equation, give the exact solution in three forms similar
Fill in the blank(s) to correctly complete each sentence.If a function ƒ has an inverse, then the graph of ƒ-1 may be obtained by reflecting the graph of ƒ across the line with equation _________.
Solve each equation.(a) x = 3log3 4 (b) logx 25 = 2 (c) log4 x = -2
Determine whether each function is one-to-one. If it is, then sketch the graph of its inverse function. y = x -- -- -- -- -
Sketch the graph of each function. Give the domain and range.ƒ(x) = log5 x
Strontium-90 decays according to the exponential function y = y0 e-0.0241t, where t is time in years. Match each question in Column I with the correct procedure in Column II to answer the question.What is the half-life of Strontium-90? A. Solve 0.75yo = Yoe-0.0241f. B. Evaluate y = 200e-0.0241(10).
Find the domain of each function. Write answers using interval notation. x2 + 7 f(x) x2 – 9
Answer each of the following.Why is log2 0 undefined?
Solve each equation. Round answers to the nearest hundredth as needed. = 64 %3D 4,
Find the inverse of each function that is one-to-one.ƒ(x) = x3 - 3
An exponential equation such as 5x = 9 can be solved for its exact solution using the meaning of logarithm and the change-of-base theorem. Because x is the exponent to which 5 must be raised in order to obtain 9, the exact solution isFor each equation, give the exact solution in three forms similar
Fill in the blank(s) to correctly complete each sentence.If ƒ(x) = x3, then ƒ-1(x) = ________.
What is the meaning of the expression log6 25?
Determine whether each function is one-to-one. If it is, then sketch the graph of its inverse function. y = x --
Solve each logarithmic equation. log 36 V6 = x r = 9A
Strontium-90 decays according to the exponential function y = y0 e-0.0241t, where t is time in years. Match each question in Column I with the correct procedure in Column II to answer the question.If the initial amount of Strontium-90 is 200 g, how much will remain after 20 yr? A. Solve 0.75yo =
Find the domain of each function. Write answers using interval notation. f(x) = Vx² – 9
Answer each of the following.How is log3 12 written in terms of natural logarithms using the change-of-base theorem?
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = - (1/3)x + 4 - 5 is that of ƒ(x) = (1/3)x reflected across the_____-axis, translated units to the left and ____units down.
Determine whether each function as graphed or defined is one-to-one. y = V3x? + 2
Match each equation in Column I with the best first step for solving it in Column II.log (2x - 1) + log (x + 4) = 1A. Use the product rule for exponents.B. Take the common logarithm on each side.C. Write the sum of logarithms as the logarithm of a product.D. Let u = ex and write the equation in
Fill in the blank(s) to correctly complete each sentence.If the point (a, b) lies on the graph of ƒ, and ƒ has an inverse, then the point ________lies on the graph of ƒ-1.
Use a calculator to evaluate each logarithm to four decimal places.(a) log 34.56 (b) ln 34.56
Determine whether each function is one-to-one. If it is, then sketch the graph of its inverse function. y = x
Solve each logarithmic equation. 16 log, 2 81
Strontium-90 decays according to the exponential function y = y0 e-0.0241t, where t is time in years. Match each question in Column I with the correct procedure in Column II to answer the question.If the initial amount of Strontium-90 is 200 g, how much will remain after 10 yr? A. Solve 0.75yo =
Find the domain of each function. Write answers using interval notation. -2 f(x) = x2 + 7
Answer each of the following.A base e logarithm is called a(n) __________ logarithm, and a base 10 logarithm is called a(n) _______ logarithm.
Fill in the blank(s) to correctly complete each sentence.The graph of ƒ(x) = 8x passes through the points (-1, _____), (0, _____), and (1, _______).
Determine whether each function as graphed or defined is one-to-one.y = (x + 3)2
Match each equation in Column I with the best first step for solving it in Column II.2e2x - 5ex - 3 = 0A. Use the product rule for exponents.B. Take the common logarithm on each side.C. Write the sum of logarithms as the logarithm of a product.D. Let u = ex and write the equation in quadratic
Fill in the blank(s) to correctly complete each sentence.The domain of ƒ is equal to the _________ of ƒ-1, and the range of ƒ is equal to the _____________ of ƒ-1.
Suppose that $15,000 is deposited in a bank certificate of deposit at an annual rate of 2.7% for 8 yr. Find the future value if interest is compounded as follows.(a) Annually (b) Quarterly (c) Monthly (d) Daily (365 days)
Determine whether each function is one-to-one. If it is, then sketch the graph of its inverse function. у3х х
Write each equivalent form.Write 103 = 1000 in logarithmic form.
A population is increasing according to the exponential functiony = 2e0.02x,where y is in millions and x is the number of years. Match each question in Column I with the correct procedure in Column II to answer the question.How large will the population be in 4 months? II A. Evaluate y =
Find the domain of each function. Write answers using interval notation. x + 2 f(x) 6. х-
Fill in the blank(s) to correctly complete each sentence.The domain of ƒ(x) = 4x is______ and the range is __________.
Determine whether each function as graphed or defined is one-to-one.y = x3 + 1
Match each equation in Column I with the best first step for solving it in Column II.e2x · ex = 2eA. Use the product rule for exponents.B. Take the common logarithm on each side.C. Write the sum of logarithms as the logarithm of a product.D. Let u = ex and write the equation in quadratic form.E.
Fill in the blank(s) to correctly complete each sentence.If two functions ƒ and g are inverses, then (ƒ ° g)(x) =___________ and_______ = x.
Graph ƒ(x) = log4 (x + 2). Give the domain and range.
The following exercises are designed to help solidify your understanding of inverse, exponential, and logarithmic functions from Sections. Determine whether the functions in each pair are inverses of each other.ƒ(x) = 3x/5 - 2, g(x) = 5 log3 (x + 2)
Write each equivalent form.Write log2 8 = 3 in exponential form.
A population is increasing according to the exponential functiony = 2e0.02x,where y is in millions and x is the number of years. Match each question in Column I with the correct procedure in Column II to answer the question.How large will the population be in 3 yr? II A. Evaluate y = 2e0.02(1/3).
Find the domain of each function. Write answers using interval notation. f(x) = |x + 4||
Answer each of the following.If ƒ(x) = 5x, what is the rule for ƒ-1(x)?
Fill in the blank(s) to correctly complete each sentence.If 0 < a < 1, then the graph of ƒ(x) = ax _____________/(rises/falls) from left to right.
Determine whether each function as graphed or defined is one-to-one. х
Match each equation in Column I with the best first step for solving it in Column II.log4 (x2 - 10) = 2A. Use the product rule for exponents.B. Take the common logarithm on each side.C. Write the sum of logarithms as the logarithm of a product.D. Let u = ex and write the equation in quadratic
Fill in the blank(s) to correctly complete each sentence.For a function to have an inverse, it must be ____________.
Graph ƒ(x) = -3x. Give the domain and range.
The following exercises are designed to help solidify your understanding of inverse, exponential, and logarithmic functions from Sections. Determine whether the functions in each pair are inverses of each other.ƒ(x) = 1 + log2 x, g(x) = 2x-1
Match the logarithm in Column I with its value in Column II. Remember that loga x is the exponent to which a must be raised in order to obtain x. II A. -2 (a) log3 81 (b) log3 3 B. -1 C. 0 (c) log10 0.01 1 D. (d) log, V6 E. 2 (e) log, 1 F. 4 (f) log, 273/2 %3D
A population is increasing according to the exponential functiony = 2e0.02x,where y is in millions and x is the number of years. Match each question in Column I with the correct procedure in Column II to answer the question.When will the population reach 3 million? II A. Evaluate y = 2e0.02(1/3).
Find the domain of each function. Write answers using interval notation. f(x) = V2x – 7
The table gives the number of representatives currently in Congress from each of five New England states. State................................................... Number of RepresentativesConnecticut .........................................................5Maine
For the logarithmic function g(x) = loga x, where a > 1, is the function increasing or decreasing over its entire domain?
Fill in the blank(s) to correctly complete each sentence.If a > 1, then the graph of ƒ(x) = ax ________/(rises/falls) from left to right.
Determine whether each function as graphed or defined is one-to-one. y х
Match each equation in Column I with the best first step for solving it in Column II.e2x-1 = 24A. Use the product rule for exponents.B. Take the common logarithm on each side.C. Write the sum of logarithms as the logarithm of a product.D. Let u = ex and write the equation in quadratic form.E.
Solve 42x+1 = 83x-6.
The following exercises are designed to help solidify your understanding of inverse, exponential, and logarithmic functions from Sections. Determine whether the functions in each pair are inverses of each other. g(x) = 8 +x f(x) = 8 – 5x, |- in
Match the logarithm in Column I with its value in Column II. Remember that loga x is the exponent to which a must be raised in order to obtain x. II A. O (a) log, 16 (b) log3 1 B. C. 4 (c) log10 0.1 (d) log, V2 D. -3 E. -1 (e) loge e2 F. -2 (f) log2 8
A population is increasing according to the exponential functiony = 2e0.02x,where y is in millions and x is the number of years. Match each question in Column I with the correct procedure in Column II to answer the question.How long will it take for the population to triple? II A. Evaluate y =
Determine whether the function represented in each table is one-to-one.The table shows the number of registered passenger cars in the United States for the years 2008–2012.Year ..............................................Registered Passenger Cars (in thousands)2008
Solve each problem.Power of a Windmill The power a windmill obtains from the wind varies directly as the cube of the wind velocity. If a wind of 10 km per hr produces 10,000 units of power, how much power is produced by a wind of 15 km per hr?
Solve each problem.If t varies inversely as s, and t = 3 when s = 5, find s when t = 20.
Environmental Pollution In situations involving environmental pollution, a costbenefit model expresses cost as a function of the percentage of pollutant removed from the environment. Suppose a cost-benefit model is expressed aswhere C(x) is cost in thousands of dollars of removing x percent of a
Pressure in a Liquid The pressure on a point in a liquid is directly proportional to the distance from the surface to the point. In a certain liquid, the pressure at a depth of 4 m is 60 kg per m2. Find the pressure at a depth of 10 m.
Solve each problem.p varies jointly as q and r2, and p = 100 when q = 2 and r = 3. Find p when q = 5 and r = 2.
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