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Chapter 3: Problem 81
Use a graphing utility to graph the function. Be sure to use an appropriate viewing window. $$f(x)=\ln (x-1)$$
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The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y=0.7979 e^{-(x-5.4)^{2} / 0.5},\) \(4 \leq x \leq 7,\) where \(x\) is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.
A sport utility vehicle that costs $$\$ 23,300$$ new has a book value of $$\$ 12,500$$ after 2 years. (a) Find the linear model \(V=m t+b\). (b) Find the exponential model \(V=a e^{k t}\) (c) Use a graphing utility to graph the two models in the same viewing window. Which model depreciates faster in the first 2 years? (d) Find the book values of the vehicle after 1 year and after 3 years using each model. (e) Explain the advantages and disadvantages of using each model to a buyer and a seller.
$$\$ 2500$$ is invested in an account at interest rate \(r\), compounded continuously. Find the time required for the amount to (a) double and (b) triple. $$r=0.045$$
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 values \(y\) (in billions of dollars) of U.S. currency in circulation in the years \(\begin{array}{lllll}2000 & \text { through } 2007 & \text { can be } & \text { modeled } & \text { by }\end{array}\) \(y=-451+444 \ln t, 10 \leq t \leq 17,\) where \(t\) represents the year, with \(t=10\) corresponding to 2000 . During which year did the value of U.S. currency in circulation exceed \$690 billion? (Source: Board of Governors of the Federal Reserve System)
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