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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.

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Presentation on theme: "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."— Presentation transcript:

1 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

2 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.?

3 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

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

6 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

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

8 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

9 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

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

11 Use the following tables to find exponential models of the given data. b x

12 Use the following tables to find exponential models of the given data. c x

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

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

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

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

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

18 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

19 Solve the following equations. a

20 Solve the following equations. b

21 Solve the following equations. c

22 Solve the following equations. d

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

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

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

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

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

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

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

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

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

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

33 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 Year Stomach Cancer Deaths

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

35 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 What would a reasonable domain and range be for the model? Year Stomach Cancer Deaths

36 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 Depth (meters) Intensity (as a %)

37 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

38 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

39 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 a. Use this model to estimate the population of Liberia in b. According to this model, what is the growth rate of Liberia’s population?

40 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

41 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

42 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?

43 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?


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