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The number of ants at a picnic is growing rapidly. At 11am 5 ants find the picnic. Each hour after 11am, 3 times as many ants have found the picnic. Let represent the number of ants at the picnic h hours after 11am. a. Write an equation for a model of. 5.1-1 1

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b. Estimate numerically when 11,000 ants will be at the picnic. c. How many ants will be at the picnic at 11 P.M.? 5.1-1 2

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A certain bacteria will double every 15 minutes. If a sample starts with 3 bacteria, find the following. a. Find an equation for a model for the number of bacteria after h hours. 5.1.2 3

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A certain bacteria will double every 15 minutes. If a sample starts with 3 bacteria, find the following: b. Find an equation for a model for the number of bacteria after n 15-minute intervals. 5.1.2 4

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c. Use your models to estimate the number of bacteria present after 5 hours. 5.1.2 5

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An isotope of hydrogen has a half life of about 4500 days. a. Find an equation for a model for the amount of remaining from a sample of 500 atoms. 5.1.3 6

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An isotope of hydrogen has a half life of about 4500 days. b. Estimate the amount of remaining after 50 years. 5.1.3 7

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In making jet fuel, kerosene is purified by removing pollutants, using a clay filter. For each foot of clay the kerosene passes through, only 80% of the pollutants remain. a. Find an equation for a model that will give the percentage of pollutants remaining after the kerosene passes through f feet of clay filter. 5.1.4 8

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When making jet fuel, kerosene is purified by removing pollutants, using a clay filter. For each foot of clay the kerosene passes through, only 80% of the pollutants remain. b. Use the model to determine the percent of pollutants remaining after passing through 3 feet of clay filter. 5.1.4 9

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Use the following tables to find exponential models of the given data. a. 5.1.5 10

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Use the following tables to find exponential models of the given data. b. 5.1.5 11 x 025 130 236 343.2 451.84

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Use the following tables to find exponential models of the given data. c. 5.1.5 12 x 03200 3800 6200 950 1212.5

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Solve the following exponential equations by inspection or trial and error. a. b. 5.2.1 13

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Solve the following exponential equations by inspection or trial and error. c. d. 5.2.1 14

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Solve the following exponential equations by inspection or trial and error. a. 5.2.2 15

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Solve the following exponential equations by inspection or trial and error. b. 5.2.2 16

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Solve the following exponential equations by inspection or trial and error. c. 5.2.2 17

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In a classroom example from section 5.1 we found the model Where n = the number of 15-minute intervals since the beginning of the experiment b(n) = number of bacteria Use this model to find the number of 15 minute intervals before there are 196,608 of these bacteria. 5.2.3 18

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Solve the following equations. a. 5.2.4 19

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Solve the following equations. b. 5.2.4 20

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Solve the following equations. c. 5.2.4 21

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Solve the following equations. d. 5.2.4 22

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Determine whether the following equations are exponential or power equations a. b. 5.2.5 23

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Sketch the graph of the following functions, by hand. Explain what the values of a and b tell you about this graph. a. 5.3.1 24

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Sketch the graph of the following functions, by hand. Explain what the values of a and b tell you about this graph. b. 5.3.1 25

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Sketch the graph of the following functions, by hand. Explain what the values of a and b tell you about this graph. a. 5.3.2 26

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Sketch the graph of the following functions, by hand. Explain what the values of a and b tell you about this graph. b. 5.3.2 27

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Find the domain and range of the following exponential functions. a. b. c. 5.3.3 28

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Sketch the graph of the given exponential functions. Write the equation for the graphs horizontal asymptote. Give the domain and range. a. 5.3.4 29

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Sketch the graph of the given exponential functions. Write the equation for the graphs horizontal asymptote. Give the domain and range. b. 5.3.4 30

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Find the exponential equation that passes through the given points. a. 5.4.1 31

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Find the exponential equation that passes through the given points. b. 5.4.1 32

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The number of deaths per 100,000 women in the United States from stomach cancer is given in the table. a. Find an equation for a model for these data. 5.4.2 33 Year1930194019501960197019801990 Stomach Cancer Deaths2821139654

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Let = the number of deaths per 100,000 women in the United States from stomach cancer. t = years since 1900. b. Estimate the number of stomach cancer deaths per 100,000 women in 2000. 5.4.2 34

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The number of deaths per 100,000 women in the United States from stomach cancer is given in the table. Let = the number of deaths per 100,000 women in the United States from stomach cancer. t = years since 1900. What would a reasonable domain and range be for the model? 5.4.3 35 Year1930194019501960197019801990 Stomach Cancer Deaths2821139654

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The intensity of light in water is decreased as you go deeper. The intensity at several depths is given in the table. a. Find an equation for a model for these data. 5.4.4 36 Depth (meters)012345 Intensity (as a %)1002561.50.40.1

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Let = The intensity of the light as a percent. d = depth in meters. b. Estimate the intensity of the light at a depth of 6 meters. c. Give a reasonable domain and range for this model. 5.4.4 37

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A swarm of 120 fruit flies in an experiment grows at a rate of about 9.8% per day. a. Find an equation for a model for the number of fruit flies in the swarm. b. Estimate the number of fruit flies in the swarm after 20 days. 5.5.1 38

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According to the CIA World Factbook 2008, the population of Liberia can be modeled by where is the population of Liberia in millions, t years since 2005. a. Use this model to estimate the population of Liberia in 2015. b. According to this model, what is the growth rate of Liberia’s population? 5.5.2 39

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The Gross Domestic Product, GDP, of Madagascar in 2005 was approximately 16.9 billion US$ and has been growing by a rate of about 6% per year. a. Find an equation for a model for the GDP of Madagascar. b. Use your model to estimate the GDP of Madagascar in 2010. 5.5.3 40

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In 2009, Serbia had a population of about 7.4million, but that population was estimated to be decreasing by approximately 0.47% per year. Source: CIA World Factbook. a. Find an equation for a model for the population of Serbia. b. Use your model to estimate the population for Serbia in 2015. 5.5.4 41

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If $30,000 is invested in a savings account that pays 4% annual interest compounded daily, what will the account balance be after 6 years? 5.5.5 42

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If $4000 is invested in a savings account that pays 2.5% annual interest compounded continuously, what will the account balance be after 9 years? 5.5.6 43

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