Chapter 1: Problem 18
In Exercises \(17-20,\) write the slope-intercept equation for the line with slope \(m\) and \(y\) -intercept \(b\) $$m=-1, \quad b=2$$
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Multiple Choice Which of the following gives the domain of \(y=2 e^{-x}-3 ?\) \((\mathbf{A})(-\infty, \infty) \quad(\mathbf{B})[-3, \infty) \quad(\mathbf{C})[-1, \infty) \quad(\mathbf{D})(-\infty, 3]\) \((\mathbf{E}) x \neq 0\)
Bacteria Growth The number of bacteria in a petri dish culture after \(t\) hours is $$B=100 e^{0.693 t}$$ (a) What was the initial number of bacteria present? (b) How many bacteria are present after 6 hours? (c) Approximately when will the number of bacteria be 200\(?\) Estimate the doubling time of the bacteria.
Multiple Choice If \(f(x)=2 x-1\) and \(g(x)=x+3,\) which of the following gives \((f \circ g)(2) ?\) (A) 2 (B) 6 (C) 7 (D) 9 (E) 10
Population of Texas Table 1.11 gives the population of Texas for several years. Population of Texas $$\begin{array}{ll}{\text { Year }} & {\text { Population (thousands) }} \\\ {1980} & {14,229} \\ {1990} & {16,986} \\ {1995} & {18,159} \\ {1998} & {20,158} \\ {1999} & {20,558} \\ {2000} & {20,852}\end{array}$$ (a) Let \(x=0\) represent \(1980, x=1\) represent \(1981,\) and so forth. Find an exponential regression for the data, and superimpose its graph on a scatter plot of the data. (b) Use the exponential regression equation to estimate the population of Texas in \(2003 .\) How close is the estimate to the actual population of \(22,119,000\) in 2003\(?\) (c) Use the exponential regression equation to estimate the annual rate of growth of the population of Texas.
In Exercises 41 and \(42,\) cvaluate the expression. $$\tan \left(\sin ^{-1}\left(\frac{9}{13}\right)\right)$$
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