Concept explainers
Reminder Round all answers to two decimal places unless otherwise indicated.
Growth of Bacteria The organism E. coli is a common bacterium. Under certain conditions, it undergoes cell division approximately each
a. Explain why the number of E. coli cells present is an exponential function of time.
b. What is the hourly growth factor for E. coli?
c. Express the population
d. How long will it take a population of E. coli to triple in size?
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Chapter 4 Solutions
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- 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?arrow_forwardHalf-Life of Radioactive Iodine A student is trying to determine the half-life of radioactive iodine-131. He measures the amount of iodine-131 in a sample solution every 8 hours. His data are shown in the table below. a Make a scatter plot of the data. b Use a calculator to find an exponential model. c Use your model to find the half-life of iodine-131. Time h Amount of 131I(g) 0 8 16 24 32 40 48 4.80 4.66 4.51 4.39 4.29 4.14 4.04arrow_forwardBuffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.arrow_forward
- U.S. Population The U.S. Constitution requires a census every 10 years. The census data for 17902010 are given in the table. a Make a scatter plot of the data. b Use a calculator to find an exponential model for the data. c Use your model to predict the population at the 2020 census. d Use your model to estimate the population in 1965. Year Population in millions Year Population in millions Year Population in millions 1790 1800 1810 1820 1830 1840 1850 1860 3.9 5.3 7.2 9.6 12.9 17.1 23.2 31.4 1870 1880 1890 1900 1910 1920 1930 1940 38.6 50.2 63.0 76.2 92.2 106.0 123.2 132.2 1950 1960 1970 1980 1990 2000 2010 151.3 179.3 203.3 226.5 248.7 281.4 308.7arrow_forward(a) How is the number e defined? (b) Given an approximate value of e, rounded to five decimal places. (c) What is the natural exponential function?arrow_forward
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