Concept explainers
Difference Quotients These exercises involve a difference quotient for an exponential function.
51. If f(x) = 10x, show that
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Chapter 4 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Difference Quotients These exercise involve a difference quotient for an exponential function. If f(x)=10x , show that f(x+h)f(x)h=10x(10x1h)arrow_forwardComparing Exponential Function In these exercises we compare the graphs of two exponential function. Sketch the graph of f(x)=xx/2 and g(x)=3x . Use the laws of Exponents to explain the relationship between these graphs.arrow_forwardComparing Exponential and Power Functions In these exercise we use a graphing calculator to compare the rates of growth of the graph of a power function and an exponential function. Compare the rates of growth of the functions f(x)=2x and g(x)=x5 by drawing the graphs of both functions in the following viewing rectangles: I. [0,5] by [0,20] II. [0,25] by [0,107] III. [0,50] by [0,108] Find the solutions of the equation 2x=x5, rounded to two decimal places.arrow_forward
- Exponential Function from a Graph Find the exponential function f(x)=ax whose graph is given.arrow_forwardRadioactive Decay The half-life of radium-226 is 1590 years. a If a sample has a mass of 150 mg, find a function that models the mass that remains after t years. b Find the mass that will remain after 1000 years. c After how many years will only 50 mg remain?arrow_forwardRadioactive Decay The half-life of radium-226 is 1590 years. (a)If a sample has a mass of 150 mg, find a function that models the mass that remains after tyears. (b)Find the mass that will remain after 1000 years. (c)After how many years will only 50 mg remain?arrow_forward
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