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Chapter 5: Q. 4 (page 256)
Given two functions f and g, the _____, denoted , is defined by____.
The answers are composition of two functions , and.
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Population Decline
The population of a midwestern city follows the exponential law.
(a) If N is the population of the city and t is the time in years, express N as a function of t.
(b) If the population decreased from 900,000 to 800,000 from 2005 to 2007, what will the population be in 2009?
A function has an inverse function. If the graph of lies in quadrant II, in which quadrant does the graph of lie?
Is there any function of the form that increases more slowly than a logarithmic function whose base is greater than 1? Explain.
A strain of E. coli SC18del-recA718 is placed into a nutrient broth at 30掳 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.
(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 e^kt.
(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.
Income Taxes The function
represents the 2011 federal income tax T (in dollars) due for a 鈥渕arried filing jointly鈥� filer whose modified adjusted gross income isg dollars, where
(a) What is the domain of the function T?
(b) Given that the tax due T is an increasing linear function of modified adjusted gross income g, find the range of the function T.
(c) Find adjusted gross income g as a function of federal income tax T. What are the domain and the range of this
function?
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