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Chapter 5: Q. 125 (page 288)
The bacteria in a -liter container double every minute. After minutes the container is full. How long did it take to fill half the container?
It will take to fill half the container.
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Population Model 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.
(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.
A fossilized leaf contains 70% of its normal amount of carbon 14.
(a) How old is the fossil? Use 5700 years as the half-life of carbon 14.
(b) Using a graphing utility, graph the relation between the percentage of carbon 14 remaining and time.
(c) Using INTERSECT, determine the time that elapses until half of the carbon 14 remains.
(d) Verify the answer found in part (a).
The graph of an exponential function is given. Match each graph to one of the following functions.
A piece of charcoal is found to contain 30% of the carbon 14 that it originally had.
(a) When did the tree from which the charcoal came die?
Use 5700 years as the half-life of carbon 14.
(b) Using a graphing utility, graph the relation between the percentage of carbon 14 remaining and time.
(c) Using INTERSECT, determine the time that elapses until half of the carbon 14 remains.
(d) Verify the answer found in part (a).
In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.
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