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mathematics
precalculus

Precalculus 9th edition Michael Sullivan - Solutions

Fill in reasons for each step in the following two solutions.Solve: log3(x €“ 1)2 = 2Both solutions given in Solution A check. Explain what caused the solution x = -2 to be lost in Solution B. Solution A log3(x – 1)2 = 2 (x – 1)2 = 32 = 9 (x – 1) = ±3 x – 1 = -3 or x – 1 = 3 -2
In problem, solve each equation.e2x+5 = 8
Is every odd function one-to-one? Explain.
If a single pane of glass obliterates 3% of the light passing through it, the percent p of light that passes through n successive panes is given approximately by the functionP(n) = 100(0.97)n(a) What percent of light will pass through 10 panes?(b) What percent of light will pass through 25 panes?
Jack and Diane live in a small town of 50 people. Unfortunately, both Jack and Diane have a cold.Those who come in contact with someone who has this cold will themselves catch the cold. The following data represent the number of people in the small town who have caught the cold after t days.Days, t
The atmospheric pressure p on a balloon or plane decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level by the functionp(h) = 760e-0.145h(a) Find the atmospheric pressure at a height of 2 kilometers (over a
In problem, solve each equation.e-2x+1 = 13
Suppose that C(g) represents the cost C, in dollars, of manufacturing g cars. Explain what C-1 (800,000) represents.
The price p, in dollars, of a Honda Civic DX Sedan that is x years old is modeled by p(x) = 16,630(0.90)x(a) How much should a 3-year-old Civic DX Sedan cost?(b) How much should a 9-year-old Civic DX Sedan cost?
In problem, solve each equation.log3(x2 + 1) = 2
Explain why the horizontal-line test can be used to identify one-to-one functions from a graph.
The normal healing of wounds can be modeled by an exponential function. If A0 represents the original area of the wound and if A equals the area of the wound, then the functionA(n) = A0e-0.35ndescribes the area of a wound after n days following an injury when no infection is present to retard the
In problem, solve each equation.log5(x2 + x + 4) = 2
Drug Medication The function D(h) = 5e-0.4h can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. How many milligrams will be present after 1 hour? After 6 hours?
In problem, solve each equation.log2 8x = -3
In problem, solve each equation.log3 3x = -1
A model for the number N of people in a college community who have heard a certain rumor isN = P(1 – e-0.15d)where P is the total population of the community and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, how many students will have heard the
In problem, solve each equation.5e0.2x = 7
Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM:F(t) = 1 - e-0.1t(a) Determine the
In problem, solve each equation.8 ∙ 102x-7 = 3
Between 5:00 PM and 6:00 PM, cars arrive at Jiffy Lube at the rate of 9 cars per hour (0.15 car per minute).The following formula from probability can be used to determine the probability that a car will arrive within t minutes of 5:00 PM:F(t) = 1 - e-0.15t (a) Determine the probability that a
In problem, solve each equation.2 ∙ 102-x = 5
Between 5:00PMand 6:00 PM, cars arrive at McDonald's drive-thru at the rate of 20 cars per hour. The following formula from probability can be used to determine the probability that x cars will arrive between 5:00PM and 6:00PM.where(a) Determine the probability that x = 15 cars will arrive between
In problem, solve each equation.4x+1 = 5
People enter a line for the Demon Roller Coaster at the rate of 4 per minute. The following formula from probability can be used to determine the probability that x people will arrive within the next minute.where(a) Determine the probability that x = 5 people will arrive within the next minute.(b)
The relative humidity is the ratio (expressed as a percent) of the amount of water vapor in the air to the maximum amount that it can hold at a specific temperature. The relative humidity, R, is found using the following formula:where T is the air temperature (in °F) and D is the dew point
Suppose that G(x) = log3(2x + 1) - 2.(a) What is the domain of G?(b) What is G(40)? What point is on the graph of G?(c) If G(x) = 3, what is x? What point is on the graph of G?(d) What is the zero of G?
Suppose that a student has 500 vocabulary words to learn. If the student learns 15 words after 5 minutes, the functionapproximates the number of words L that the student will learn after t minutes.(a) How many words will the student learn after 30 minutes?(b) How many words will the student learn
Suppose that F(x) = log2(x + 1) - 3.(a) What is the domain of F?(b) What is F(7)? What point is on the graph of F?(c) If F(x) = -1, what is x? What point is on the graph of F?(d) What is the zero of F?
The equation governing the amount of current I (in amperes) after time t (in seconds) in a single RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in volts) is(a) If E = 120 volts, R = 10 ohms, and L = 5 henrys, how much current h is $[1 – e (R/L\¥] R$
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. SIn(-x) if x < 0 | f(x) = if x > 0 | In x
The equation governing the amount of current I (in amperes) after time t (in microseconds) in a single RC circuit consisting of a resistance R (in ohms), a capacitance C (in microfarads), and an electromotive force E (in volts) is(a) If E = 120 volts, R = 2000 ohms, and C = 1.0 micro farad, how
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts.
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if 0 < x < 1 if x 2 1 x
If f is an exponential function of the form f(x) = C ∙ ax with growth factor 3 and f(6) = 12, what is f(7)?
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if 0 < x < 1 In x f(x) = -In x if x 2 1
Use a calculator to compute the values offor n = 4, 6, 8, and 10. Compare each result with e. 2 + 2! 3! n!
Chemistry The pH of a chemical solution is given by the formulapH = -log10[He+]where [H+] is the concentration of hydrogen ions in moles per liter. Values of pH range from 0 (acidic) to 14 (alkaline).(a) What is the pH of a solution for which [He+] is 0.1?(b) What is the pH of a solution for which
Use a calculator to compute the various values of the expression. Compare the values to e. 2 + 1 1 + 1 2 + 2 3 + 3 4 + 4 etc.
If f(x) = ax, show that f(x + h) – f(x) d – 1 a*. h + 0
The atmospheric pressure p on an object decreases with increasing height. This pressure, measured in millimeters of mercury, is related to the height h (in kilometers) above sea level by the functionp(h) = 760e-0.145h(a) Find the height of an aircraft if the atmospheric pressure is 320 millimeters
If f(x) = ax, show that f(A + B) = f (A) ∙ f(B).
The normal healing of wounds can be modeled by an exponential function. If A0 represents the original area of the wound and if A equals the area of the wound, then the functionA(n) = A0e-0.35ndescribes the area of a wound after n days following an injury when no infection is present to retard the
If f(x) = ax, show that f(-x) = 1/f(x).
Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00 PM.F(t) = 1 – e-0.1t(a) Determine how many
If f(x) = ax, show that f(αx) = [f(x)]α.
Between 5:00 PM and 6:00 PM, cars arrive at Jiffy Lube at the rate of 9 cars per hour (0.15 car per minute).The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 5:00 PM.F(t) = 1 – e-0.15t(a) Determine how many minutes are needed
Problem provide definitions for two other transcendental functions.The hyperbolic sine function, designated by sinh x, is defined as(a) Show that f(x) = sinh x is an odd function.(b) Graph f(x) = sinh x using a graphing utility. (e* – e*) - e sinh x (et
The formula D = 5e-0.4h can be used to find the number of milligrams D of a certain drug that is in a patient’s bloodstream h hours after the drug was administered.When the number of milligrams reaches 2, the drug is to be administered again. What is the time between injections?
Problem provide definitions for two other transcendental functions.The hyperbolic cosine function, designated by cosh x, is defined as(a) Show that f(x) = cosh x is an even function.(b) Graph f(x) = coshx using a graphing utility.(c) Refer to problem 122. Show that, for every x,Data from problem
A model for the number N of people in a college community who have heard a certain rumor isN = P(1 – e-0.15d)where P is the total population of the community and d is the number of days that have elapsed since the rumor began. In a community of 1000 students, how many days will elapse before 450
Pierre de Fermat (1601€“1665) conjectured that the function
The equation governing the amount of current I (in amperes) after time t (in seconds) in a simple RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys), and an electromotive force E (in volts) isIf E = 12 volts, R = 10 ohms, and L = 5 henrys, how long does it take to
The bacteria in a 4-liter container double every minute.After 60 minutes the container is full. How long did it take to fill half the container?
Psychologists sometimes use the functionL(t) = A(1 – e-kt)to measure the amount L learned at time t. The number A represents the amount to be learned, and the number k measures the rate of learning. Suppose that a student has an amount A of 200 vocabulary words to learn. A psychologist determines
Normal conversation: intensity of x = 10-7 watt per square meter.The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x/I0, where Io = 10-12 watt per square meter is the least intense sound that a human ear can
Amplified rock music: intensity of 10-1 watt per square meter.The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x/I0, where I0 = 10-12 watt per square meter is the least intense sound that a human ear can detect.
As the base a of an exponential function f(x) = ax, where a > 1 increases, what happens to the behavior of its graph for x > 0? What happens to the behavior of its graph for x < 0?
The graphs of y = a-x and y = (1/a)x are Identical. Why?
Heavy city traffic: intensity of x = 10-3 watt per square meter.The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log x/I0, where I0 = 10-12 watt per square meter is the least intense sound that a human ear can
Diesel truck traveling 40 miles per hour 50 feet away: intensity 10 times that of a passenger car traveling 50 miles per hour 50 feet away whose loudness is 70 decibels.The loudness L(x), measured in decibels (dB), of a sound of intensity x, measured in watts per square meter, is defined as L(x) =
Mexico City in 1985: seismographic reading of 125,892 millimeters 100 kilometers from the center. In problem use the following discussion: The Richter scale is one way of converting seismographic readings into numbers that provide an easy reference for measuring the magnitude M of an earthquake.
San Francisco in 1906: seismographic reading of 50,119 millimeters 100 kilometers from the center. In problem use the following discussion: The Richter scale is one way of converting seismographic readings into numbers that provide an easy reference for measuring the magnitude M of an earthquake.
The concentration of alcohol in a person’s bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the formR = ekxwhere x is the percent of concentration of alcohol in the bloodstream and k is a constant.(a) Suppose
In the definition of the logarithmic function, the base a is not allowed to equal 1. Why?
In buying a new car, one consideration might be how well the price of the car holds up over time. Different makes of cars have different depreciation rates. One way to compute a depreciation rate for a car is given here. Suppose that the current prices of a certain automobile are as shown in the
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function.{(-2, 1), (-3, 2), (-10, 0), (1, 9), (2, 4)}
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function.{(-2, 2), (-1, 6), (0, 8), (1, -3), (2, 9)}
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log4(x2 - 9) - log4(x + 3) = 3
In problem, find the domain of each logarithmic function.F(x) = log5(2x + 1)
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.x ……………………….. g(x)-1
8% compounded semiannually or 7.9% compounded dailyIn problem, determine the rate that represents the better deal.
In problem, find the exact value of each logarithm without using a calculator.log1/2 16
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function.{(-3, 5), (-2, 9), (-1, 2), (0, 11), (1, -5)}
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log1/3(x2 + x) - log1/3(x2 - x) = -1
In problem, find the domain of each logarithmic function.f(x) = log(3x - 2)
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.x ……………………….. f(x)-1
9% compounded monthly or 8.8% compounded dailyIn problem, determine the rate that represents the better deal.
In problem, find the exact value of each logarithm without using a calculator.log3 (1/9)
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function. Unemployment Rate State 11% 5.5% 5.1% 6.3% Virginia Nevada Tennessee Техas
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log2(x + 1) + log2(x + 7) = 3
In problem, find the domain of the composite function f ° g.f(x) = x2 + 4; g(x) = √x - 2
In problem, convert each logarithmic statement to an equivalent statement involving an exponent.loga 4 = 3
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.x ……………………….. F(x)-1
9% compounded quarterly or 9¼%compounded annuallyIn problem, determine the rate that represents the better deal.
In problem, find the exact value of each logarithm without using a calculator.log5 25
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function. Monthly Cost of Life Insurance Age 30 $7.09 $8.40 $11.29 40 45
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.log3(x + 1) + log3(x + 4) = 2
In problem, convert each logarithmic statement to an equivalent statement involving an exponent.log5 u = 13
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.x ……………………….. g(x)-1
6%compounded quarterly or 6¼%compounded annuallyIn problem, determine the rate that represents the better deal.
In problem, find the exact value of each logarithm without using a calculator.log8 8
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function. Domestic Gross (in millions) Title Star Wars $461 Star Wars: Episode One – The Phantom Menace $431 E.T. the Extra Terrestrial $400 Jurassic Park $357 Forrest Gump $330
In problem, solve each logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places.In(x + 1) - In x = 2
In problem, find the domain of the composite function f ° g.f(x) = x - 2; g(x) = √1 - x
In problem, convert each exponential statement to an equivalent statement involving a logarithm.a5 = m
In problem, determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.x ……………………….. g(x)-1
For 6% compounded continuouslyIn problem, find the effective rate of interest.
In problem, find the exact value of each logarithm without using a calculator.log2 1
In problem, find the inverse of each one-to-one function. State the domain and the range of each inverse function. Annual Rainfall (inches) Location Mt Waialeale, Hawaii 460.00 Monrovia, Liberia 202.01 Pago Pago, American Samoa 196.46 Moulmein, Burma 191.02 Lae, Papua New Guinea 182.87

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