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mathematics
college algebra
College Algebra 12th edition Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels - Solutions
Connecting Graphs with Equations Write an equation for the graph given. Each represents a logarithmic function ƒ with base 2 or 3, translated and/or reflected. y |x = 3 (7, 1) (5,0) (4, –1)
Connecting Graphs with Equations Write an equation for the graph given. Each represents a logarithmic function ƒ with base 2 or 3, translated and/or reflected. х*-114 _x =. (7, 0) х (1,–2) (0,–3)
To graph the function ƒ(x) = -log5 (x - 7) - 4, reflect the graph of y = log5 x across the_________ -axis, then shift the graph _______units to the right and ________ units down.
Graph the function.ƒ(x) = log1/2 (x + 3) - 2
Graph the function.ƒ(x) = log2 (x + 2) - 3
Consider the function(a) What are the domain and range of ƒ?(b) Explain why ƒ-1 exists.(c) Write an equation for ƒ-1(x).(d) What are the domain and range of ƒ-1?(e) Graph both ƒ and ƒ-1. How are the two graphs related with respect to the line y = x? f(x) = V2x – 7.
Graph the function.ƒ(x) = log3 (x - 1) + 2
Graph the function.ƒ(x) = log1/3 (3 - x)
Graph the function.ƒ(x) = log1/2 (1 - x)
Graph the function.ƒ(x) = log6 (x - 2)
Graph the function.ƒ(x) = log5 (x + 1)
Graph the function.ƒ(x) = log10 x
Graph the function.ƒ(x) = log5 x
In Exercise, match the function with its graph from choices A–F.ƒ(x) = log2 (-x) A. B. C. х х х F. E. D. х х HНE
In Exercise, match the function with its graph from choices A–F.ƒ(x) = log2 (x - 1) A. B. C. х х х F. E. D. х х HНE
In Exercise, match the function with its graph from choices A–F. f(x) = log, A. B. C. х х х D. E. F. х х HНE
In Exercise, match the function with its graph from choices A–F.
In Exercise, match the function with its graph from choices A–F.ƒ(x) = log2 2x A. B. C. х х х F. E. D. х х HНE
In Exercise, match the function with its graph from choices A–F.ƒ(x) = log2 x A. B. C. D. E. F. 1/2
Graph the function. Give the domain and range.ƒ(x) = | log1/2 (x - 2)|
Graph the function. Give the domain and range.ƒ(x) = log1/2 (x - 2)
Graph the function. Give the domain and range.ƒ(x) = (log1/2 x) - 2
Graph the function. Give the domain and range.ƒ(x) = |log2 (x + 3)|
Graph the function. Give the domain and range.ƒ(x) = log2 (x + 3)
Graph the function. Give the domain and range.ƒ(x) = (log2 x) + 3
Solve the equation.4x - 24 = logx 1 (x > 0, x ≠ 1)
Solve the equation.3x - 15 = logx 1 (x > 0, x ≠ 1)
Solve the equation.log(x-4) 19 = 1
Solve the equation.log(x+3) 6 = 1
Solve the equation.log1/3 (x + 6) = -2
Solve the equation.log1/2 (x + 3) = -4
Solve the equation. log4 x =
Solve the equation. log, x :
Solve the equation. x = log, V25
Solve the equation. x = log, V16 (16
Solve the equation.log2 x = 3
Solve the equation.log4 x = 3
Solve the equation.logx 16 = -2
Solve the equation.logx 25 = -2
Solve the equation. x = glogs 11
Solve the equation. |x = 2log2 9
Solve the equation. x = 12l0812 5
Solve the equation. х3D 3logs 8
The height of a certain tree in feet after x years is modeled by(a) Make a table for ƒ starting at x = 10, and incrementing by 10. What appears to be the maximum height of the tree?(b) Graph ƒ and identify the horizontal asymptote. Explain its significance.(c) After how many years was the tree 30
Solve each problem that uses a logistic function.As age increases, so does the likelihood of coronary heart disease (CHD). The fraction of people x years old with some CHD is modeled by(a) Evaluate ƒ(25) and ƒ(65) to the nearest hundredth. Interpret the results.(b) At what age, to the nearest
Suppose a conservation campaign, together with higher rates, caused demand for electricity to increase at only 2% per year. Find the number of years, to the nearest tenth, before twice as much electricity would be needed.
Suppose that in a certain area the consumption of electricity has increased at a continuous rate of 6% per year. If it continued to increase at this rate, find the number of years, to the nearest tenth, before twice as much electricity would be needed.
Assume the cost of a loaf of bread is $4. With continuous compounding, find the number of years, to the nearest tenth, it would take for the cost to triple at an annual inflation rate of 4%.
Use the sales decline function given in Exercise. If a = 0.10, S0 = 50,000, and t is time measured in years, find the number of years it will take for sales to fall to half the initial sales. Round the answer to the nearest tenth.
Sales of a product, under relatively stable market conditions but in the absence of promotional activities such as advertising, tend to decline at a constant yearly rate. This rate of sales decline varies considerably from product to product, but it seems to remain the same for any particular
The U.S. Consumer Price Index for the years 1990–2013 is approximated by A(t) = 100e0.0264t, where t represents the number of years after 1990. (Since A(16) is about 153, the amount of goods that could be purchased for $100 in 1990 cost about $153 in 2006.) Use the function to determine the year
Many environmental situations place effective limits on the growth of the number of an organism in an area. Many such limited-growth situations are described by the logistic functionAssume that G0 = 100, M = 2500, k = 0.0004, and x = time in decades (10-yr periods).(a) Use a calculator to graph the
Drug effectiveness decreases over time. If, each hour, a drug is only 90% as effective as the previous hour, at some point the patient will not be receiving enough medication and must receive another dose. If the initial dose was 200 mg and the drug was administered 3 hr ago, the expression
How long will it take the bacteria population in Exercise 47 to double? Round the answer to the nearest tenth.
The growth of bacteria makes it necessary to time-date some food products so that they will be sold and consumed before the bacteria count is too high. Suppose for a certain product the number of bacteria present is given by ƒ(t) = 500e0.1t, where t is time in days and the value of ƒ(t) is in
Refer to Exercise 45 and determine how long it will take, to the nearest day, for the initial number of people susceptible to decrease to half its amount.Exercise 45During an epidemic, the number of people who have never had the disease and who are not immune (they are susceptible) decreases
During an epidemic, the number of people who have never had the disease and who are not immune (they are susceptible) decreases exponentially according to the function ƒ(t) = 15,000e-0.05t, where t is time in days. Find the number of susceptible people at each time.(a) At the beginning of the
The number of views of a YouTube video increases after the number of hours posted as shown in the table.Hour ................Number of Views20 ..................................10025 ..................................51730 ................................201535
Student enrollment in the Wentzville School District, one of the fastest-growing school districts in the state of Missouri, has projected growth as shown in the graph.(a) Use the model y = y0 ekx to find an exponential function that gives the projected enrollment y in school year x. Let the school
The number of years, n, since two independently evolving languages split off from a common ancestral language is approximated by n ≈ -7600 log r, where r is the proportion of words from the ancestral language common to both languages. Find each of the following to the nearest year.(a) Find n if r
Average annual per-household spending on housing over the years 2000–2012 is approximated by H = 12,744e0.0264t, where t is the number of years since 2000. Find H to the nearest dollar for each year.(a) 2005 (b) 2009 (c) 2012
Personal consumption expenditures for recreation in billions of dollars in the United States during the years 2000–2013 can be approximated by the function A(t) = 632.37e0.0351t, where t = 0 corresponds to the year 2000. Based on this model, how much were personal consumption expenditures in 2013
Out-of-pocket spending in the United States for health care increased between 2008 and 2012. The function ƒ(x) = 7446e0.0305x models average annual expenditures per household, in dollars. In this model, x represents the year, where x = 0 corresponds to 2008.(a) Estimate out-of-pocket household
A midwestern city finds its residents moving to the suburbs. Its population is declining according to the function P(t) = P0 e-0.04t, where t is time measured in years and P0 is the population at time t = 0. Assume that P0 = 1,000,000.(a) Find the population at time t = 1 to the nearest
In 2000 India’s population reached 1 billion, and it is projected to be 1.4 billion in 2025.(a) Find values for P0 and a so that P(x) = P0 ax-2000 models the population of India in year x. Round a to five decimal places.(b) Predict India’s population in 2020 to the nearest tenth of a
Use the model in Exercise 35 to determine the year in which the number of continuously serving members was 338.Exercise 35The turnover of legislators is a problem of interest to political scientists. It was found that one model of legislative turnover in a particular body was M(t) =
The turnover of legislators is a problem of interest to political scientists. It was found that one model of legislative turnover in a particular body was M(t) = 434e-0.08t, where M(t) represents the number of continuously serving members at time t. Here, t = 0 represents 1965, t = 1 represents
Use the Table feature of a graphing calculator to find how long it will take $1500 invested at 2.75% compounded daily to triple in value. Zoom in on the solution by systematically decreasing the increment for x. Find the answer to the nearest day. (Find the answer to the nearest day by eventually
How long will it take an investment to triple if interest is compounded continuously at 3%?
If interest is compounded continuously and the interest rate is tripled, what effect will this have on the time required for an investment to double?
Find the doubling time of an investment earning 2.5% interest if interest is compounded continuously.
If Russ (see Exercise 29) chooses the plan with continuous compounding, how long will it take for his $60,000 to grow to $70,000?Exercise 29Russ, who is self-employed, wants to invest $60,000 in a pension plan. One investment offers 3% compounded quarterly. Another offers 2.75% compounded
Russ, who is self-employed, wants to invest $60,000 in a pension plan. One investment offers 3% compounded quarterly. Another offers 2.75% compounded continuously.(a) Which investment will earn more interest in 5 yr?(b) How much more will the better plan earn?
A piece of metal is heated to 300°C and then placed in a cooling liquid at 50°C. After 4 min, the metal has cooled to 175°C. Find its temperature to the nearest hundredth after 12 min.
Boiling water, at 100°C, is placed in a freezer at 0°C. The temperature of the water is 50°C after 24 min. Find the temperature of the water to the nearest hundredth after 96 min.
The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model A(t) = 10e0.0095t.At what temperature will 15 g dissolve?
Paint from the Lascaux caves of France contains 15% of the normal amount of carbon-14. Estimate the age of the paintings.
A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 of a contemporary sample. How old was the sample?
Find the domain of the function. Write answers using interval notation.ƒ(x) = ln (x2 + 1)
Consider ƒ(x) = log4 (2x2 - x).(a) Use the change-of-base theorem with base e to write log4 (2x2 - x) in a suitable form to graph with a calculator.(b) Graph the function using a graphing calculator. Use the window [-2.5, 2.5] by [-5, 2.5].(c) What are the x-intercepts?(d) Give the equations of
The traditional IRA (individual retirement account) is a common tax-deferred saving plan in the United States. Earned income deposited into an IRA is not taxed in the current year, and no taxes are incurred on the interest paid in subsequent years. However, when the money is withdrawn from the
Computing power has increased dramatically as a result of the ability to place an increasing number of transistors on a single processor chip. The table lists the number of transistors on some popular computer chips made by Intel.(a) Make a scatter diagram of the data. Let the x-axis represent the
The table shows the total payroll (in millions of dollars) of the Chicago Cubs baseball team for the years 2010–2014.Year ......................................Total Payroll (millions of dollars)2010 ...........................................................145.42011
After a medical drug is injected directly into the bloodstream, it is gradually eliminated from the body. Graph the following functions on the interval 30, 104. Use 30, 5004 for the range of A(t). Determine the function that best models the amount A(t) (in milligrams) of a drug remaining in the
Suppose the inflation rate is 4%. Use the formula for continuous compounding to find the number of years, to the nearest tenth, for a $1 item to cost $2.
Anne deposits $12,000 for 8 yr in an account paying 2.5% interest compounded annually. She then leaves the money alone with no further deposits at 3% interest compounded annually for an additional 6 yr. Find the total amount on deposit after the entire 14-yr period.
Manuel deposits $10,000 for 12 yr in an account paying 3% interest compounded annually. He then puts this total amount on deposit in another account paying 4% interest compounded semiannually for another 9 yr. Find the total amount on deposit after the entire 21-yr period.
Find the number of years (to the nearest tenth) needed for $48,000 to become $53,647 at 2.8% interest compounded semiannually.
What annual interest rate, to the nearest tenth, will produce $4700 if $3500 is left at interest compounded annually for 10 yr?
The San Francisco earthquake of 1906 had a Richter scale rating of 8.3.(a) Express the magnitude of this earthquake in terms of I0 to the nearest hundred thousand.(b) In 1989, the San Francisco region experienced an earthquake with a Richter scale rating of 7.1. Express the magnitude of this
The magnitude of an earthquake, measured on the Richter scale, is log I/I0, where I is the amplitude registered on a seismograph 100 km from the epicenter of the earthquake, and I0 is the amplitude of an earthquake of a certain (small) size. On August 24, 2014, the Napa Valley in California was
Decibel rating of the loudness of a sound is modeled bywhere I is the intensity of a particular sound, and I0 is the intensity of a very faint threshold sound. A few years ago, there was a controversy about a proposed government limit on factory noise. One group wanted a maximum of 89 decibels,
Use a graphing calculator to solve the equation ex = 4 - ln x. Give solution(s) to the nearest thousandth.
Solve the equation. Give solutions in exact form.D = 200 + 100 log x, for x
Solve the equation. Give solutions in exact form. for Io |d = 10 log -
Solve the equation. Give solutions in exact form. for n S = a In 1 + (;-)m:
Solve the equation. Give solutions in exact form.ln [ln e-x] = ln 3
Solve the equation. Give solutions in exact form. |log 16 Vx + 1 = 4
Solve the equation. Give solutions in exact form.ln (6x) - ln (x + 1) = ln 4
Solve the equation. Give solutions in exact form.log7 (3x + 2) - log7 (x - 2) = 1
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