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Chapter 3: Problem 1
Approximate each number using a calculator. Round your answer to three decimal places. $$2^{3.4}$$
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Determine whether each statement makes sense or does not make sense, and explain your reasoning. I use the natural base \(e\) when determining how much money I'd have in a bank account that earns compound interest subject to continuous compounding.
Explain the differences between solving \(\log _{3}(x-1)=4\) and \(\log _{3}(x-1)=\log _{3} 4\)
In parts (a)-(c), graph \(f\) and \(g\) in the same viewing rectangle. a. \(f(x)=\ln (3 x), g(x)=\ln 3+\ln x\) b. \(f(x)=\log \left(5 x^{2}\right), g(x)=\log 5+\log x^{2}\) c. \(f(x)=\ln \left(2 x^{3}\right), g(x)=\ln 2+\ln x^{3}\) d. Describe what you observe in parts (a)-(c). Generalize this observation by writing an equivalent expression for \(\log _{b}(M N),\) where \(M>0\) and \(N>0\) e. Complete this statement: The logarithm of a product is equal to____.
Graph each of the following functions in the same viewing rectangle and then place the functions in order from the one that increases most slowly to the one that increases most rapidly. $$y=x, y=\sqrt{x}, y=e^{x}, y=\ln x, y=x^{x}, y=x^{2}$$
The formula \(A=25.1 e^{0.0187 t}\) models the population of Texas, \(A\), in millions, \(t\) years after 2010 . a. What was the population of Texas in \(2010 ?\) b. When will the population of Texas reach 28 million?
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