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All Textbook Solutions for College Algebra (MindTap Course List)

41E 42E 43E 44E 45E 46E 47E 48E 49E 50E 51E 52E 53E 54E 55E 56E 57E 58E 59E 60E 61E 62E Write a third-degree polynomial function with real coefficients and the given zeros. 4,i Write a third-degree polynomial function with real coefficients and the given zeros. 5,i 65E 66E 67E 68E 69E 70E 71E 72E 73E 74E 75E 76E 77E 78E 79E 80E 81E 82E 83E 84E 85E 86E 87E 88E 89E 90E 91E 92E 93E 94E 95E 96E Graph each rational function. f(x)=x(x1)2 98E 99E 100E 1CT 2CT 3CT 4CT Assume that an object tossed vertically upward reaches a height of h feet after t seconds, where h=100t16t2. What is that maximum height?Assume that an object tossed vertically upward reaches a height of h feet after t seconds, where h=100t16t2. Suspension bridges The cable of a suspension bridge is in the shape of the parabola x22500y+25,000=0 in the coordinate system shown in the illustration. Distances are in feet. How far above the roadway is the cables lowest point?7CT 8CT 9CT 10CT 11CT 12CT 13CT 14CT Let P(x)=3x32x2+4. Use synthetic division to find each value. P(13)16CT 17CT 18CT 19CT 20CT 21CT 22CT 23CT 24CT 25CT 26CT 27CT 28CT 29CT 30CT Self Check 1 Approximate each expression correct to 4 decimals. a. 53/5 b. -36 c. 7-2.356 2SC 3SC 4SC 5SC 6SC 7SC 8SC Fill in the blanks. If b0 and b1,fx=bx represents and ____ function.Fill in the blanks. If fx=bx represents an increasing function, then b____.Fill in the blanks. In interval notation, the domain of the exponential function fx=bx is ____.Fill in the blanks. The number b is called the ____ of the exponential function fx=bx.Fill in the blanks. The range of the exponential function fx=bx is ____.6E Fill in the blanks. If b0 and b1, the graph of fx=bx approaches the x-axis, which is called a horizontal ____ of the curve.8E Fill in the blanks. If b1, then fx=bx defines a an ____ function.Fill in the blanks. The graph of an exponenetial function fx=bx always passes through the points 0,1 and ____.Fill in the blanks. To two decimal places, the value of e is ____.Fill in the blanks. The continuous compound interest formula is A= _____.13E 14E Practice Use a calculator to find each value to four decimal places. 43 16E Practice Use a calculator to find each value to four decimal places. 7 Practice Use a calculator to find each value to four decimal places. 3-19E 20E 21E 22E Practice Find f0and f2 for each of the given exponential functions. fx=5x 24E Practice Find f0and f2 for each of the given exponential functions. fx=13-x 26E Practice Graph each exponential function. fx=3x 28E 29E 30E 31E 32E 33E 34E 35E 36E 37E 38E Practice Determine whether the graph could represent an exponential function of the form fx=bx.40E Practice Determine whether the graph could represent an exponential function of the form fx=bx.42E Practice Find the value of b, if any, that would cause the graph of fx=bx to look like the graph indicated.44E Practice Find the value of b, if any, that would cause the graph of fx=bx to look like the graph indicated.46E Practice Find the value of b, if any, that would cause the graph of fx=bx to look like the graph indicated.48E Practice Find the value of b, if any, that would cause the graph of fx=bx to look like the graph indicated.50E Graph each function by using transformations. fx=3x-1 52E Graph each function by using transformations. fx=2x+1 54E 55E 56E 57E 58E 59E 60E 61E 62E Graph each function by using transformations. fx=2x+1-2 64E Graph each function by using transformations. fx=3x-2+1 66E 67E 68E 69E 70E 71E 72E Use a graphing calculator to graph each function. fx=52x 74E 75E 76E Use a graphing calculator to graph each function. fx=2ex 78E Use a graphing calculator to graph each function. fx=5e-0.5x 80E Applications In Exercises 81-84, assume that there are no deposits or withdrawals. Compound interest An initial deposit of 10,000 earns 8% interest, compounded quarterly. How much will be in the account in 10 years?82E Applications In Exercises 81-84, assume that there are no deposits or withdrawals. Compound interest rates How much more interest could 500 earns in 5 years, compounded semi-annually two times a year, if the annual interest rate were 512% instead of 5%?84E Applications Compound interest If 1 had been invested on July 4,1776, at 5% interest, compounded annually, what would it be worth on July 4,2076?86E 87E 88E Applications Continuous compound interest An initial investment of 5000 earns 8.2% interest, compounded continuously. What will the investment be worth in 12 years?90E Applications Comparison of compounding methods An initial investment of 5000 grows at an annual rate of 8.5% for 5 years. Compare the final balances resulting from continuous compounding and annual compounding.92E 93E Applications Determining an initial deposit An account now contains 11,180 and has been accumulating interest at 7% annual rate, compounded continuously, for 7 years. Find the initial deposit.Applications Saving for college In 20 years, a father wants to accumulate 40,000 to pay for his daughters college expenses. If he can get 6% interest, compounded quarterly, how much must he invest now to achieve his goal?96E 97E 98E 99E 100E 101E 102E 103E 104E 105E 106E 107E 108E 109E 110E 111E 112E 113E 114E Self Check After 800 years, how much radium will remain?2SC 3SC 4SC 5SC 1E 2E Use a calculator to help solve each problem. Tritium decay Tritium, a radioactive isotope of hydrogen, has a half-life of 12.4 years. Of an initial sample of 50 grams, how much remain after 100 years?4E 5E 6E 7E 8E Use a calculator to help solve each problem. Drug absorption in smokers The biological half-life of the asthma medication theophylline is 4.5 hours for smokers. Find the amount of the drug retained in smokers system 12 hours after a dose of 1 unit is taken.Use a calculator to help solve each problem. Drug absorption in nonsmokers For a nonsmoker, the biological half-life of theophylline is 8 hours. Find the amount of the drug retained in nonsmokers system 12 hours after taking one-unit dose.11E Use a calculator to help solve each problem. Oceanography At one location in the Atlantic Ocean, I0=14 lumens and k=0.7. Find the intensity of light at a depth of 12 meters. See Exercise 11.Use a calculator to help solve each problem. Oceanography At a depth of 3 meters at one location in the Pacific Ocean, the intensity I of light is 1 lumen and k=0.5.Find the intensity I0 of light at the surface.Use a calculator to help solve each problem. Oceanography At a depth of 2 meters at one location off the coast of Belize, the intensity I of light is 2 lumen and k=0.2. Find the intensity I0 of light at the surface.Use a calculator to help solve each problem. Bluegill population A Wisconsin lake is stocked with 10,000 bluegill. The population is expected to grow exponentially according to the model Pt=P02t/2. How many bluegill will be in the lake in 5 years?16E 17E 18E 19E 20E 21E Use a calculator to help solve each problem. Alcohol absorption In one individual, the percent of alcohol absorbed into the bloodstream after drinking two glasses of wine is given by the following formula. Find the percent of alcohol absorbed into the blood after 12 hour. Pt=0.31-e-0.05t where, t is in minutes 23E Use a calculator to help solve each problem. World population growth See Exercise 23. Assuming a Malthusian growth model, find the world population in 40 years. 23. World population growth The population of the Earth is approximately 6 billion people and is growing at an annual rate of 1.9%. Assuming a Malthusian growth model, find the world population in 30 years.25E 26E 27E 28E 29E 30E 31E 32E 33E 34E 35E Use a calculator to help solve each problem. Life expetctancy The life expectancy l of white females can be estimated by using the function lx=78.51.001x, where x is the current age. Find the life expectancy of a white female who is currently 50 years old. Give the answer to the nearest tenth.37E 38E 39E Use a calculator to help solve each problem. Free-falling objects After t seconds, a certain falling object has a velocity v given by vt=501-e-0.3t. Which is falling faster after 2 seconds, this object or the skydiver in Exercise 38? 38. Sky diving Before the parachute opens, the velocity v in meters per second of a skydiver is given by vt=501-e-0.2t. Find the initial velocity.41E 42E 43E Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?45E 46E 47E 48E Graph the following logistic function, first discussed in Example 5. Use window settings of 0,20 for x and 0,1,500,000 for y. Pt=1,200,0001+1199e-0.4t 50E 51E 52E Self Check Write 13-2=1169 in logarithmic form.Self Check Write log5625=4 in exponential form.3SC 4SC 5SC 6SC 7SC 8SC 9SC 10SC 1E 2E 3E 4E 5E 6E 7E 8E 9E 10E 11E 12E 13E 14E 15E 16E 17E 18E 19E Write each equation in logarithmic form. 3-4=181 21E

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