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Chapter 12: Problem 9
Write each equation in its equivalent logarithmic form. $$2^{3}=8$$
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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. $$y=x, y=\sqrt{x}, y=e^{x}, y=\ln x, y=x^{x}, y=x^{2}$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\log _{2} 8}{\log _{2} 4}=\frac{8}{4}$$
The formula \(A=10 e^{-0.003 t}\) models the population of Hungary, \(A\), in millions, \(t\) years after 2006 . a. Find Hungary's population, in millions, for \(2006,2007\), \(2008,\) and \(2009 .\) Round to two decimal places. b. Is Hungary's population increasing or decreasing?
Complete the table for a savings account subject to n compounding periods per year \(\left[A=P\left(1+\frac{r}{n}\right)^{n t}\right]\) Round answers to one decimal place. $$\begin{array}{l|c|l|l|l} \hline \begin{array}{l} \text { Amount } \\ \text { Invested } \end{array} & \begin{array}{l} \text { Number of } \\ \text { Compounding } \\ \text { Periods } \end{array} & \begin{array}{l} \text { Annual Interest } \\ \text { Rate } \end{array} & \begin{array}{l} \text { Accumulated } \\ \text { Amount } \end{array} & \begin{array}{l} \text { Time } t \\ \text { in Years } \end{array} \\ \hline \$ 1000 & 360 & & \$ 1400 & 2 \\ \hline \end{array}$$
Without using a calculator, find the exact value of $$\frac{\log _{3} 81-\log _{\pi} 1}{\log _{2 \sqrt{2}} 8-\log 0.001}$$
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