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Chapter 3: Problem 11
Write the logarithmic equation in exponential form. For example, the exponential form of \(\log _{5} 25=2\) is \(5^{2}=25\). $$\log _{32} 4=\frac{2}{5}$$
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Gaussian models are commonly used in probability and statistics to represent populations that are ________ ________.
Rewrite each verbal statement as an equation. Then decide whether the statement is true or false. Justify your answer. The logarithm of the quotient of two numbers is equal to the difference of the logarithms of the numbers.
Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln (x+5)=\ln (x-1)-\ln (x+1)$$
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?
The yield \(V\) (in millions of cubic feet per acre) for a forest at age \(t\) years is given by \(V=6.7 e^{-48.1 / t}\) (a) Use a graphing utility to graph the function. (b) Determine the horizontal asymptote of the function. Interpret its meaning in the context of the problem. (c) Find the time necessary to obtain a yield of 1.3 million cubic feet.
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