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mathematics
precalculus

Questions and Answers of Precalculus

The value V of a Honda Civic DX that is t years old can be modeled by V(t) = 16,775(0.905)t.(a) According to the model, when will the car be worth $15,000?(b) According to the model, when will the
In problem, solve each equation.e-2x = 1/3
In problem, graph each function. Based on the graph, state the domain and the range and find any intercepts. if x < 0 -e f(x) = if x 2 0 -et
Give an example of a function whose domain is the set of real numbers and that is neither increasing nor decreasing on its domain, but is one-to-one.
The following data represent the wind speed (mph) and wind chill factor at an air temperature of 15°F.(a) Using a graphing utility, draw a scatter diagram with wind speed as the independent
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
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
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
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
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
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) =
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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) =
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
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
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) =
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
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) =
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
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
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
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
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
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
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
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
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
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 =
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
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,
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,
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,
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,
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
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

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