Chapter 5: Problem 100
Explain why \(\log _{a} x\) is defined only for \(01\).
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Chapter 5: Problem 100
Explain why \(\log _{a} x\) is defined only for \(01\).
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The table of values was obtained by evaluating a function. Determine which of the statements may be true and which must be false. $$ \begin{array}{|l|l|l|l|} \hline x & 1 & 2 & 8 \\ \hline y & 0 & 1 & 3 \\ \hline \end{array} $$ (a) \(y\) is an exponential function of \(x\). (b) \(y\) is a logarithmic function of \(x\). (c) \(x\) is an exponential function of \(y\). (d) \(y\) is a linear function of \(x\).
Compound Interest In Exercises 57-60, complete the table to determine the balance \(A\) for $$\$ 12,000$$ invested at rate \(r\) for \(t\) years, compounded continuously. \(\begin{array}{|l|l|l|l|l|l|} \hline t & 10 & 20 & 30 & 40 & 50 \\ \hline A & & & & & \\ \hline \end{array}\) $$ r=6 \% $$
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$ \ln \frac{6}{\sqrt{x^{2}+1}} $$
Compound Interest In Exercises 57-60, complete the table to determine the balance \(A\) for $$\$ 12,000$$ invested at rate \(r\) for \(t\) years, compounded continuously. \(\begin{array}{|l|l|l|l|l|l|} \hline t & 10 & 20 & 30 & 40 & 50 \\ \hline A & & & & & \\ \hline \end{array}\) $$ r=4 \% $$
The population \(P\) (in millions) of Russia from 1996 to 2004 can be approximated by the model \(P=152.26 e^{-0.0039 t}\), where \(t\) represents the year, with \(t=6\) corresponding to 1996 . (Source: Census Bureau, International Data Base) (a) According to the model, is the population of Russia increasing or decreasing? Explain. (b) Find the population of Russia in 1998 and \(2000 .\) (c) Use the model to predict the population of Russia in \(2010 .\)
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