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mathematics
mathematical applications for the management

Questions and Answers of Mathematical Applications for the Management

In Problems, solve each equation.3 + 2log2 x = log2(x + 3) + 5
In Problems, solve each equation.ln (2x - 1) - ln 3 = ln 9
Use the following information to answer Problems. World population can be considered as growing according to the equationN = N0(1 + r)twhere N0 is the number of individuals at time t = 0, r is the
Use the following information to answer Problems. World population can be considered as growing according to the equationN = N0(1 + r)twhere N0 is the number of individuals at time t = 0, r is the
In Problems, solve each equation.log3(4x - 5) = 3
Write each expression in Problems as the sum or difference of two logarithmic functions containing no exponents.log5 (x2 / √x + 4)
Using U.S. Department of Health and Human Services data for selected years from 1960 and projected to 2024, the national out-of-pocket expenditures for health care H can be modeled byH =
In Problems, solve each equation.312 = 300 + 300e-0.08x
If the supply function for a product is given by p = 200(2q), where q represents the number of hundreds of units, what will be the price when the producers are willing to supply 500 units?
If $1000 is invested for x years at 10%, compounded continuously, the future value that results isS = 1000e0.10xWhat amount will result in 5 years?
Disposable income is the amount available for spending and saving after taxes have been paid and is one gauge for the state of the economy. Using U.S. Energy Administration data for selected years
If f (x) = 10x, find f (log 2).
The purchasing power P of a fixed income of $30,000 per year (such as a pension) after t years of 4% inflation can be modeled byP = 30,000 (1.04)-tFind the purchasing power (to the nearest dollar)
For the years from 2002 and projected to 2024, the total national health care expenditures H, in billions of dollars, can be modeled by H = 1500e0.053t where t is the number of years past 2000.
If f (x) = ex, find f (ln 3).
If $1000 is invested for x years at 8%, compounded quarterly, the future value is given by S = 1000(1.02)4x What amount will result in 8 years?
The population of a certain city grows according to the formula y = P0e0.03t. If the population was 250,000 in 2015, estimate the year in which the population reaches 350,000.
If f (x) = log (x), find f (10-7).
The following table gives the projected population, in thousands, of Americans over 100 years of age.(a) Create an exponential function that models this population as a function of the number of
In Problems, use a graphing utility to graph the functions.Given f(x) = 3x. Graph y = f(x) and y = f(x - h) = 3x - h for each h, where h = 4, 1, -2, and -5. Explain the effect that h has on the
If f (x) = log (x), find f (10x).
The total U.S. personal income I (in billions of dollars) from 1960 and projected to 2024 can be modeled bywhere t is the number of years after 1960.(a) What does the model predict the total U.S.
If f (x) = ln (x), find f (ex).
Given f (x) = 4x. Graph y = f(x) and y = f(x) + C = 4x + C for each C, where C = -5, -2, 3, and 6.
The supply function for x units of a certain product is given by p = 10 + 6 ln(3x + 10)(a) Find the price per unit when 30 units are supplied.(b) If the price per unit is $43, find the number of
If f (x) = ln x, find f (e-2).
A company plans to phase out one model of its product and replace it with a new model. An advertising campaign for the product being replaced just ended, and typically after such a campaign, monthly
The total national health expenditures per capita (in dollars) for 2006 and projected to 2021 can be modeled with the equationH(t) = 6791e0.04343twhere t is the number of years past 2005.(a) Find the
In Problems, graph each function.y = ln (-x)
With data from the U.S. Energy Information Administration, the following figure shows a scatter plot of tons of carbon dioxide (CO2) emissions per person for selected years from 2010 and projected to
Given that y = (4/5)x, write an equivalent equation in the form y = a-x, with a > 1.
In Problems, graph each function.y = log2 (-x)
The graph in the following figure shows the number of active workers who will be (or have been) supporting each Social Security beneficiary. What type of function might be an appropriate model for
Solve for x: 47,500 = 1500(1.015)6x
Write log4 (x3 + 1) as a base e logarithm using a change-of-base formula.
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.ln (x + 2) + ln x = ln (x + 12)
Write ln (M · N) as a sum involving M and N.
In Problems, simplify the expressions using properties or definitions of logarithms.ln ex2
In Problems, graph each function.y = 5e-x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12. 3 log x + 10 = log(3x) + 14
In Problems, evaluate each logarithm without using a calculator. In Problems 13–17, check with the change-of-base formula.10log 3.15
In Problems, simplify the expressions using properties or definitions of logarithms.log7 73
In Problems, graph each function.y = 3-2x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.7 + log(8x) = 25 - 2 log x
In Problems, evaluate each logarithm without using a calculator. In Problems 13–17, check with the change-of-base formula.eln 5
In Problems, simplify the expressions using properties or definitions of logarithms.eln x4
In Problems 9–20, graph each function.y = 3-x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.ln x + ln 8 = 5
In Problems, write the equation in logarithmic form. 91/2 = 3
In Problems, evaluate each logarithm without using a calculator. In Problems 13–17, check with the change-of-base formula.ln e
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.log4x - log4(x + 3) = log4(x - 2)
Write ln (x3 - 1 / x + 2) as a difference involving two binomials.
In Problems, simplify the expressions using properties or definitions of logarithms.log2 8
In Problems, graph each function.y = 2ex
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.ln x - ln 5 = 10
In Problems, write the equation in logarithmic form.4-1 = 1/4
In Problems, solve each equation for x to three decimal places.8 - log3(5x - 13) = 5
In Problems, graph each function.y = 3x-1
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.log5(x + 2) = 2
In Problems, solve each equation for x to three decimal places.3 + 6e-2x = 7
In Problems, graph each function.y = 5-x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.log4(9x + 1) = 3
Write 32x = 27 in logarithmic form.
In Problems, graph each function.y = (2/3)x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.lnx = 8
In Problems, solve for x by writing the equation in exponential form.ln (2 - x) = -1.4 (to three decimal places)
Use the definition of a logarithmic function to write log7 x = 3.1 in exponential form. Then find x to three decimal places.
In Problems, graph each function.y = (4/5)x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.log x = 5
In Problems, solve for x by writing the equation in exponential form.ln (2x + 5) = 2.2 (to three decimal places)
In Problems, use a calculator to give a decimal approximation of the numbers to three decimal places.log 21
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.150 = 200/1 + 30e-0.3x
In Problems, solve for x by writing the equation in exponential form.log (1.34 - x) = -1
Graph the following functions.y = 10(2-x)
In Problems, use a calculator to give a decimal approximation of the numbers to three decimal places.ln 4
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.55 = 60/1 + 5e-0.6x
In Problems, solve for x by writing the equation in exponential form.log (4x - 7) = 2
Graph the following functions.y = log x
In Problems, use a calculator to give a decimal approximation of the numbers to three decimal places.3-2.1
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.500 = 600 - 600e-0.4x
In Problems 5–14, solve for x by writing the equation inexponential form.log3 (7 - x) = 3
Graph the following functions.y = 3-2x
In Problems, use a calculator to give a decimal approximation of the numbers to three decimal places.e4
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.78 = 100 - 100e-0.01x
In Problems 5–14, solve for x by writing the equation inexponential form.log7 (3x + 1) = 2
In Problems, use technology to graph the functions.y = log7 x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.2500 = 600e0.05x
Graph the following functions.y = ln x
In Problems, use technology to graph the functions.y = e2x
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.10,000 = 1500e0.10x
In Problems, solve for x by writing the equation in exponential form.log16x = -1/2
Graph the following functions.y = 1/2(4x)
In Problems, use technology to graph the functions.y = ln (0.5x)
In Problems, solve each equation. Give answers correct to three decimal places in Problems 1–12.75,000 = 15,000(1.02)4x
Graph the following functions.y = 2x
In Problems, use technology to graph the functions.y = 30.5x
In Problems, graph the functions.y = ln x
In Problems, use the definition of a logarithmic function to rewrite each equation in exponential form.-2 = log3 (1/9)
In Problems, graph the functions.y = log5 x
In Problems, graph the functions.y = 3-x

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