Log-log and Semilog Graph Paper Problem: Let f(x) = 1000 0.65x be the number of bacteria

Chapter 7, Problem C.2

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Log-log and Semilog Graph Paper Problem: Let f(x) = 1000 0.65x be the number of bacteria remaining in a culture over time, x, measured in hours. Let g(x) = 0.09x2 be the area of skin measured in square centimeters on a snake of length x, measured in centimeters. Figure 7-7d shows the graph of the exponential function f plotted on semilog graph paper. Figure 7-7e shows the graph of the power function g plotted on log-log graph paper. On these graphs, one or both of the axes have scales proportional to the logarithm of the variables value. Thus the scales are compressed so that a wide range of values can fit on the same sheet of graph paper. For these two functions, the graphs are straight lines. a. Read the values of f(9) and g(60) from the graphs. Then calculate these numbers using the given equations. If your graphical answers are different from the calculated answers, explain what mistakes you made in reading the graphs. b. Youll need a sheet of semilog graph paper and a sheet of log-log graph paper for graphing. On the semilog paper, plot the function h(x) = 2 1.5x using several values of x in the domain [0, 15]. On the log-log paper, plot the function p(x) = 700x1.3 using several values of x in the domain [1, 100]. What do the graphs of the functions look like? f(x) is a linear function of x.Explain how this is connected to the shape of the graph. d. Take the logarithm of both sides of the equation g(x) = 0.09x2. Use the properties of logarithms to show that log g(x) is a linear function of log x. How does this relate to the graph in Figure 7-7e?