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Chapter 3: Problem 47
Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\log _{8} x^{4}$$
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The graph of a Gaussian model is ________ shaped, where the ________ ________ is the maximum -value of the graph.
The management at a plastics factory has found that the maximum number of units a worker can produce in a day is \(30 .\) The learning curve for the number \(N\) of units produced per day after a new employee has worked \(t\) days is modeled by \(N=30\left(1-e^{k t}\right) .\) After 20 days on the job, a new employee produces 19 units. (a) Find the learning curve for this employee (first, find the value of \(k\) ). (b) How many days should pass before this employee is producing 25 units per day?
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$6 \log _{3}(0.5 x)=11$$
Complete the table for the time \(t\) (in years) necessary for \(P\) dollars to triple if interest is compounded continuously at rate \(r\). $$ \begin{array}{|l|l|l|l|l|l|l|} \hline r & 2 \% & 4 \% & 6 \% & 8 \% & 10 \% & 12 \% \\ \hline t & & & & & & \\ \hline \end{array} $$
The number \(y\) of hits a new search-engine website receives each month can be modeled by \(y=4080 e^{k t},\) where \(t\) represents the number of months the website has been operating. In the website's third month, there were 10,000 hits. Find the value of \(k,\) and use this value to predict the number of hits the website will receive after 24 months.
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