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College Algebra With Modeling And Visualization 6th Edition Gary Rockswold - Solutions

Solve each equation. Approximate answers to four decimal places when appropriate. 2 In 3x = 8
Use the compound interest formula to approximate the final value of each amount.$1600 at 1.3% compounded monthly for 2.5 years
The population P (in millions) of Georgia x years after 2010 can be modeled by the equation P = 9.7e0.017x.(a) Use properties of logarithms to solve this equation for x. (b) Use your new equation to find x when P = 12. Interpret your answer.
Use the compound interest formula to approximate the final value of each amount.$2000 at 8.7% compounded annually for 5 years
Determine when 85% of the hits, or engagements, are remaining.
Use the table for f(x) to find a table for f-1(x). Identify the domains and ranges of f and f-1. 10 100 012 X 1 f(x) 0
Find f(x) and g(x) so that h(x) = (g ° f)(x). _h(x) = -4x + 1
Solve each equation. Approximate answers to four decimal places when appropriate. 4log₂x = 16
When light passes through water, its intensity I decreases according to the formula I(x) = I0e-kx, where I0 is the initial intensity of the light and x is the depth in feet. If I0 = 1000 lumens per square meter and k = 0.12, determine the depth at which the intensity is 25% of I0.
Use the compound interest formula to approximate the final value of each amount.$500 at 0.8% compounded semiannually for 20 years
Use the table for f(x) to find a table for f-1(x). Identify the domains and ranges of f and f-1. x 0 f(x) 0 2 4 4 16
Find f(x) and g(x) so that h(x)=(g ° f)(x). h(x) = 5√x - 1
Solve each equation. Approximate answers to four decimal places when appropriate. log, 5x = 10
Use the compound interest formula to approximate the final value of each amount.$750 at 0.5% compounded monthly for 3 years
Let I(x) = 500e-0.2x and determine the depth x at which the intensity I is 1% of I0 = 500.
Use the table for f(x) to find a table for f-1(x). Identify the domains and ranges of f and f-1. r 0 1 f(x) 1 2 2 4
Find f(x) and g(x) so that h(x)=(g ° f)(x). h(x): 1 (x - 1)²
Solve each equation. Approximate answers to four decimal places when appropriate. 5 In (2x) + 6 = 12
Use the compound interest formula to approximate the final value of each amount.$1500 at 0.75% compounded continuously for 8 years
According to Moore's law the number of transistors that can be placed on an integrated circuit has doubled every 2 years. In 1971 there were only 2300 transistors on an integrated circuit. (a) Find an exponential function T(x) = Cax that gives the number of transistors on an integrated circuit
Use f(x) to complete the table. f(x) = 4x X f-¹(x) 0 2 4 6
Find f(x) and g(x) so that h(x)=(g ° f)(x). I+x=zx 2 = (x)4
Solve each equation. Approximate answers to four decimal places when appropriate. 16-4ln 3x = 2
Use f(x) to complete the table. f(x) = x x-8 f'(x) -1 8 27
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
Find f(x) and g(x) so that h(x)=(g ° f)(x). h(x) = x³/4x1/4
Solve each equation. Approximate answers to four decimal places when appropriate. 9 - 3log, 2x = 3
Find f(x) and g(x) so that h(x)=(g ° f)(x). h(x) = x2/3 – 5xl/3 + 4
Solve each equation. Approximate answers to four decimal places when appropriate. 7log (4x) + 5 = -2
Use the compound interest formula to approximate the final value of each amount.$900 at 0.99% compounded continuously for 9 years
Use the formula E(x) = 1000(258)x to determine when 1 billion computations could first be performed with 1 kilowatt-hour.
There is a relationship between perceived corruption and human development in a country that can be mod- eled by H(x) = 0.3 +0.28 Inx. In this formula x represents the Corruption Perception Index, where 1 is very corrupt and 10 is least corrupt. The out- put gives the Human Development Index, which
If college tuition is currently $8000 per year, inflating at 6% per year, what will be the cost of tuition in 10 years?
How long does it take for an investment to double its value if the interest is 12% compounded annually? 6% compounded annually?
The percentage of Brazil's population that lives in urban areas can be modeled by U(x) = 72 + 4.33 Inx, where x ≥ 1 is the number of years after 1990. (a) Evaluate U(24) and interpret the result.(b) Predict when urbanization will first reach 88%.
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
Find values for a and b so that f(x) models the data exactly. f(x)= a + blog.x 1 10 f(x) 5 7 X 100 9
Write the sum log 1 + 2log 2 + 3log 3 + 4log 4 + 5log 5 as a logarithm of a single expression.
Determine a profit function P that results if the albums are sold for $15 each. Find the profit from selling 3000 albums.
Determine the best investment: compounding continuously at 6.0% or compounding annually at 6.3%.
The number of Atlantic bluefin tuna in thousands x years after 1974 can be modeled by f(x) = 230(0.881)x. Estimate the year when the number of bluefin tuna reached 95 thousand.
Graph y = f(x) and y = x. Then graph y = f-1(x). f(x) = -x + 1
A student insists that log(x + y) and logx + logy are equal. How could you convince the student otherwise?
Graph y = f(x) and y = x. Then graph y = f-1(x). f(x) = x³ - 1
Graph y = f(x) and y = x. Then graph y = f-1(x). 1-XA f(x) = √x-1
Graph y = f(x) and y = x. Then graph y = f-1(x). f(x) = (x + 1)², x = -1
Explain how to find verbal, numerical, graphical, and symbolic representations of an inverse function. Give examples.
Can a one-to-one function have more than one x-intercept or more than one y-intercept? Explain.
If the graphs of y = f-1(x) and y = f(x) intersect at a point (a, b), what can be said about these graphs? Explain.
If f(x) = ax2 + bx + c with a ≠ 0, does f-1(x) exist? Explain.
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
Show thatequals 2. What is the domain of the given expression? √x² - 4) + log₂ (x - √x² - 4) log₂ (x + √x +
Use the graph off to sketch a graph of f-1. Give a symbolic representation of f-1. -3 432 f(x)=e* 1 3
Suppose that for a major production company it costs $150,000 to produce a master track for a music video and $1.50 to produce each copy. (a) Write a cost function C that outputs the cost of producing the master track and x copies. (b) If the music videos are sold for $6.50 each, find a
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
Find values for a and b so that f(x) models the data exactly. f(x) = a + blog₂ x 1 2 4 6 8.9 x f(x) 3.1
There are 36 inches in a yard and 2.54 centimeters in an inch. (a) Write a function I that converts x yards to inches. (b) Write a function C that converts x inches to centimeters. (c) Express a function F that converts x yards to centimeters as a composition of two
Use the graph off to sketch a graph of f-1. Give a symbolic representation of f-1.
There are 4 quarts in 1 gallon, 4 cups in 1 quart, and 16 tablespoons in 1 cup. (a) Write a function that converts x gallons to quarts. (b) Write a function C that converts x quarts to cups. (c) Write a function T that converts x cups to table- spoons. (d) Express a function F
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
In 2000 the population of India reached 1 billion, and in 2025 it is projected to be 1.4 billion. (a) Find values for Cand a so that P(x) = Cax-2000 models the population of India in year x. (b) Estimate India's population in 2010. (c) Use P to determine the year when India's
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
A sample of bacteria taken from a river has an initial concentration of 2.5 million bacteria per milliliter and its concentration triples each week. (a) Find an exponential model B that calculates the concentration after x weeks. (b) Estimate the concentration after 1.5 weeks.
Determine the best investment: compounding quarterly at 3.1% or compounding daily at 2.9%.
In 2007 the population of Pakistan was 164 million, and it is expected to be 250 million in 2025. (a) Approximate C and a so that P(x) = Cax-2007 models these data, where P is in millions and x is the year. (b) Estimate the population of Pakistan in 2015, and compare your estimate to the
The number N of E. coli bacteria in millions per milliliter after t minutes can be modeled by N(t) = 0.50.014t Determine symbolically the elapsed time required for the concentration of bacteria to reach 25 million per milliliter.
A pan of boiling water with a temperature of 212°F is set in a bin of ice with a temperature of 32°F. The pan cools to 70°F in 30 minutes. (a) Find T0, D, and a so that T(1) = T0 + Dat models the data, where / is in hours. (b) Find the temperature of the pan after 10 minutes. (c)
Use the tables to evaluate the following. x012 3 5 f(x) 1 1 2 0 2 1 x-1 3 4 3 4 4 2 4 5
Use the graph off to sketch a graph of f-1. Give a symbolic representation of f-1. 1 f(x) = log₂ x 2 x
A fish population in a small lake is estimated to be 6000. Due to a change in water quality, this population is decreasing by half each year. (a) Find an exponential model f that approximates the number of fish in the lake after x years. (b) Estimate the fish population to the nearest
Use the tables to evaluate the following. 0 f(x) 8 X x 2 2 0 2 8 g(x) 4 4 6 0 6 4 0 6 2 8 4 8 6
Use the graph off to sketch a graph of f-1. Give a symbolic representation of f-1. f(x) = log x 2
If a driver attempts to stop while traveling at x miles per hour on dry, level pavement, the reaction distance is r(x) = 11/5x and the braking distance is b(x) = 1/11x2, where both distances are in feet. (a) Write a formula for a functions in terms of r(x) and b(x) that gives the stopping
In Example 10, f and g are both linear. (a) Find symbolic representations for f and g. (b) Determine (g ° f)(x). (c) Evaluate (g ° f) (3.5) and interpret the result. EXAMPLE 10 Evaluating a composite function numerically Depletion of the ozone layer can cause an increase in the amount of UV
A driver's reaction distance is r(x) = 11/6x and braking distance is b(x) = 1/9x2. (a) Find a formula s (x) that computes the stopping distance for this driver traveling at x miles per hour. (b) Evaluates (60) and interpret the result.
A student insists that log(x/y) and log x/log y are equal. How could you convince the student otherwise?
A pan of cold water with a temperature of 35°F is brought into a room with a temperature of 75°F. After 1 hour, the temperature of the pan of water is 45°F. (a) Find T0, D, and a so that T(t) = T0 + Dat models the data, where is in hours. (b) Find the temperature of the water after 3
Graph y = f(x). Is f increasing or decreasing on its domain? f(x) = log₁/2 x
Use the tables to evaluate the following. 0 f(x) 8 X x 2 2 0 2 8 g(x) 4 4 6 0 6 4 0 6 2 8 4 8 6
A fish fly density is 2 million insects per acre and is decreasing by one-fourth (25%) every week. Estimate their density after 3.2 weeks.
Graph y = f(x). Is f increasing or decreasing on its domain? f(x) = log₁/3 x
A concentration of bacteria is 5 million per milliliter and is tripling every day. Estimate the concentration after 2.4 days.
Use the tables to evaluate the following. 0 f(x) 8 X x 2 2 0 2 8 g(x) 4 4 6 0 6 4 0 6 2 8 4 8 6
Suppose that a can of soda, initially at 5°C, warms to 18°C after 2 hours in a room that has a temperature of 20°C. (a) Find the temperature of the soda can after 1.5 hours. (b) How long did it take for the soda to warm to 15°C?
If possible, calculate the composition and interpret the result. (a) (g ° f)(1) (b) (f ° g)(21)
A stock is worth $40 a share and decreases by 2% per week. Estimate its value after 6.5 weeks.
A soda can at 80°F is put into a cooler containing ice at 32°F. Its temperature after 1 minutes is T(t) = 32 + 48 (0.9)t. (a) Evaluate T (30) and interpret your results. (b) How long did it take for the soda to cool to 50°F?
A home is worth $200,000 and decreases in value by 1.5% per year. Estimate its value after 3.5 years.
Urban areas tend to be warmer than the surrounding rural areas. This effect is called the urban heat island. In the first figure, f computes the average increase in nighttime summer temperatures in degrees Celsius at Sky Harbor Airport in Phoenix from 1948 to 1990. In this graph, 1948 is the base
Complete the following. (a) Graph y = f(x), y = f-1(x), and y = x. (b) Determine the intervals where f and f-1 are increasing or decreasing. f(x) = log, x
Use the tables to evaluate the following. 0 f(x) 8 X x 2 2 0 2 8 g(x) 4 4 6 0 6 4 0 6 2 8 4 8 6
Complete the following. (a) Graph y = f(x), y = f-1(x), and y = x. (b) Determine the intervals where f and f-1 are increasing or decreasing. f(x) = log₁/2 x
The intensity I of sunlight at the surface of a lake is 300 watts per square meter. For each 1-foot increase in depth of a lake, the intensity of sunlight decreases by a factor of 9/10.(a) Estimate the intensity I of sunlight at a depth of 50 feet. (b) Graph the intensity of sunlight to a
In the figures. f computes the cubic feet of water in a pool after x days, and g converts cubic feet to gallons.(a) Find the gallons of water in the pool after 2 days. (b) Interpret (g ° f)(x). Water (cubic feet) 6000 5000 4000 3000 2000 1000 0 y = f(x) T 2 3 4 Time (days) 5
Use transformations to graph y = g(x). Give the equation of any asymptotes. g(x) = log(x - 2)
Use the tables to evaluate the following. 0 f(x) 8 X x 2 2 0 2 8 g(x) 4 4 6 0 6 4 0 6 2 8 4 8 6
The function f computes the temperature on a summer day after x hours, and g converts Fahrenheit temperature to Celsius temperature. See the figures.(a) Evaluate (g ° f)(2). (b) Interpret (g ° f)(x). Temperature (°F) Temperature (°C) 84 64 0 40 35 30 25 20 15 10 5 1.0 20 y = f(x) Time
Use the tables to evaluate the following. 0 f(x) 8 X x 2 2 0 2 8 g(x) 4 4 6 0 6 4 0 6 2 8 4 8 6
In one study, the life spans of 129 robins were monitored over a 4-year period. The equationcan be used to calculate the number of years y required for x percent of the robin population to die. For example, to find the time when 40% of the robins had died, substitute x = 40 into the equation. The
Use transformations to graph y = g(x). Give the equation of any asymptotes. g(x) = log(x + 2)

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