A strain of E. coli SC18del-recA718 is placed into a

A strain of E. coli Beu 397-recA441 is placed into a nutrient broth at 30 Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Time (hours), x Population, y Source:Dr. Polly Lavery, Joliet Junior College 0 2.5 3.5 4.5 6 0.09 0.18 0.26 0.35 0.50 (a) Draw a scatter diagram treating time as the independent variable. (b) Using a graphing utility, build an exponential model from the data. (c) Express the function found in part (b) in the form N1t2 = N0 ekt. (d) Graph the exponential function found in part (b) or (c) on the scatter diagram. (e) Use the exponential function from part (b) or (c) to predict the population at x = 7 hours. (f) Use the exponential function from part (b) or (c) to predict when the population will reach 0.75.

A strain of E. coli SC18del-recA718 is placed into a nutrient broth at 30 Celsius and allowed to grow. The data below are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Time (hours), x Population, y 2.5 3.5 4.5 4.75 5.25 0.175 0.38 0.63 0.76 1.20 Source: Dr. Polly Lavery, Joliet Junior College (a) Draw a scatter diagram treating time as the independent variable. (b) Using a graphing utility, build an exponential model from the data. (c) Express the function found in part (b) in the form N(t) = N0 ekt. (d) Graph the exponential function found in part (b) or (c) on the scatter diagram. (e) Use the exponential function from part (b) or (c) to predict the population at x = 6 hours. (f) Use the exponential function from part (b) or (c) to predict when the population will reach 2.1.

A chemist has a 100-gram sample of a radioactive material. He records the amount of radioactive material every week for 7 weeks and obtains the following data: Week Weight (in Grams) 0 1 2 3 69.4 100.0 88.3 75.9 4 5 59.1 51.8 6 45.5 (a) Using a graphing utility, draw a scatter diagram with week as the independent variable. (b) Using a graphing utility, build an exponential model from the data. (c) Express the function found in part (b) in the form A1t2 = A0 ekt. (d) Graph the exponential function found in part (b) or (c) on the scatter diagram. (e) From the result found in part (b), determine the half-life of the radioactive material. (f) How much radioactive material will be left after 50 weeks? (g) When will there be 20 grams of radioactive material?

The following data represent the number of cigarettes (in billions) exported from the United States by year. Source: Statistical Abstract of the United States, 2006 Year Cigarette Exports (in billions of pieces) 1995 1998 1999 2000 147.9 231.1 201.3 151.4 2001 2002 133.9 127.4 2003 121.5 2004 118.7 (a) Let t = the number of years since 1995. Using a graphing utility, draw a scatter diagram of the data using t as the independent variable and number of cigarettes as the dependent variable. (b) Using a graphing utility, build an exponential model from the data. (c) Express the function found in part (b) in the form A1t2 = A0ekt. (d) Graph the exponential function found in part (b) or (c) on the scatter diagram.

The following data represent the price and quantity demanded in 2009 for Dell personal computers. Price ($/Computer) Quantity Demanded 2300 2000 1700 1500 171 152 159 164 1300 1200 1000 176 180 189 (a) Using a graphing utility, draw a scatter diagram of the data with price as the dependent variable. (b) Using a graphing utility, build a logarithmic model from the data. (c) Using a graphing utility, draw the logarithmic function found in part (b) on the scatter diagram. (d) Use the function found in part (b) to predict the number of Dell personal computers that will be demanded if the price is $1650.

The following data represent the price and quantity supplied in 2009 for Dell personal computers. Price ($/Computer) Quantity Supplied 2300 2000 1700 1500 150 180 173 160 1300 1200 1000 137 130 113 (a) Using a graphing utility, draw a scatter diagram of the data with price as the dependent variable. (b) Using a graphing utility, build a logarithmic model from the data. (c) Using a graphing utility, draw the logarithmic function found in part (b) on the scatter diagram. (d) Use the function found in part (b) to predict the number of Dell personal computers that will be supplied if the price is $1650.

The following data represent the population of the United States. An ecologist is interested in building a model that describes the population of the United States. 344 CHAPTER 5 Exponential and Logarithmic Functions Year Population 1900 1910 1920 1930 1940 1950 1960 76,212,168 92,228,496 106,021,537 123,202,624 132,164,569 151,325,798 1970 1980 179,323,175 203,302,031 226,542,203 1990 248,709,873 2010 308,745,538 2000 281,421,906 Source: U.S. Census Bureau (a) Using a graphing utility, draw a scatter diagram of the data using years since 1900 as the independent variable and population as the dependent variable. (b) Using a graphing utility, build a logistic model from the data. (c) Using a graphing utility, draw the function found in part (b) on the scatter diagram. (d) Based on the function found in part (b), what is the carrying capacity of the United States? (e) Use the function found in part (b) to predict the population of the United States in 2012. (f) When will the United States population be 350,000,000? (g) Compare actual U.S. Census figures to the predictions found in parts (e) and (f). Discuss any differences

The following data represent the world population. An ecologist is interested in building a model that describes the world population. Year Population (in Billions) 2001 2002 2003 2004 2005 2006 2007 6.17 6.25 6.32 6.40 6.48 6.55 2008 2010 6.85 2009 6.63 6.71 6.79 Source: U.S. Census Bureau (a) Using a graphing utility, draw a scatter diagram of the data using years since 2000 as the independent variable and population as the dependent variable. (b) Using a graphing utility, build a logistic model from the data. (c) Using a graphing utility, draw the function found in part (b) on the scatter diagram. (d) Based on the function found in part (b), what is the carrying capacity of the world? (e) Use the function found in part (b) to predict the population of the world in 2015. (f) When will world population be 10 billion?

The following data represent the world population. An ecologist is interested in building a model that describes the world population. Year Population (in Billions) 2001 2002 2003 2004 2005 2006 2007 6.17 6.25 6.32 6.40 6.48 6.55 2008 2010 6.85 2009 6.63 6.71 6.79 Source: U.S. Census Bureau (a) Using a graphing utility, draw a scatter diagram of the data using years since 2000 as the independent variable and population as the dependent variable. (b) Using a graphing utility, build a logistic model from the data. (c) Using a graphing utility, draw the function found in part (b) on the scatter diagram. (d) Based on the function found in part (b), what is the carrying capacity of the world? (e) Use the function found in part (b) to predict the population of the world in 2015. (f) When will world population be 10 billion?

The following data represent the number of basic cable TV subscribers in the United States. A market researcher believes that external factors, such as satellite TV, have affected the growth of cable subscribers. She is interested in building a model that can be used to describe the number of cable TV subscribers in the United States. (a) Using a graphing utility, draw a scatter diagram of the data using the number of years after 1970, t, as the independent variable and number of subscribers as the dependent variable. (b) Using a graphing utility, build a logistic model from the data. (c) Using a graphing utility, draw the function found in part (b) on the scatter diagram. (d) Based on the model found in part (b), what is the maximum number of cable TV subscribers in the United States? (e) Use the model found in part (b) to predict the number of cable TV subscribers in the United States in 2015.

The following data represent the age and average total cholesterol for adult males at various ages. Age Total Cholesterol 189 205 215 210 210 194 27 40 50 60 70 80 (a) Using a graphing utility, draw a scatter diagram of the data using age, x, as the independent variable and total cholesterol, y, as the dependent variable. (b) Based on the scatter diagram drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between age and total cholesterol. Be sure to justify your choice of model. (c) Using a graphing utility, find the model of best fit. (d) Using a graphing utility, draw the model of best fit on the scatter diagram drawn in part (a). (e) Use your model to predict the total cholesterol of a 35-year-old male

The following data represent crime rate against individuals (crimes per 1000 households) and their income (in dollars) in the United States in 2007. (a) Using a graphing utility, draw a scatter diagram of the data using income, x, as the independent variable and crime rate, y, as the dependent variable. (b) Based on the scatter diagram drawn in part (a), decide on a model (linear, quadratic, cubic, exponential, logarithmic, or logistic) that you think best describes the relation between income and crime rate. Be sure to justify your choice of model. (c) Using a graphing utility, find the model of best fit. (d) Using a graphing utility, draw the model of best fit on the scatter diagram drawn in part (a). (e) Use your model to predict the crime rate of a household whose income is $55,000. Income C

The following data represent the asking price and age of a Chevrolet Impala SS. Age Asking Price 1 1 2 2 $23,195 $27,417 $26,750