LEARNING CURVES The American Court Reporter Institute finds that the average student taking Elementary Machine Shorthand will progress at a rate given by
in a 20-week course, where Q(t) measures the number of words of dictation a student can take per minute after t weeks in the course. If the average student can take 50 words of dictation per minute after 10 weeks in the course, how many words per minute can the average student take after completing the course?
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Chapter 9 Solutions
Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)
- Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forwardSize of High Schools The farm population has declined dramatically in the years since World War II, and with that decline, rural school districts have been faced with consolidating in order to be economically efficient. One researcher studied data from the early 1960s on expenditures for high schools ranging from 150 to 2400 in enrollment. He considered the cost per pupil as a function of the number of pupils enrolled in the high school, and he found the approximate formula C=7430.402n+0.00012n2 where n is the number of pupils enrolled and C is the cost, in dollars, per pupil. a. Make a graph of C versus n. b. What enrollment size gives a minimum per-pupil cost? c. If a high school had an enrollment of 1200, how much in per-pupil cost would be saved by increasing enrollment to the optimal size found in part b?arrow_forwardMaximum Profit The profit P (in dollars) generated by selling x units of a certain commodity ¡s given by P(x)=1500+12x0.0004x2 What is the maximum profit, and how many units must be sold to generate it?arrow_forward
- Suppose that the price per unit in dollars ofa cell phone production is modeled by p=450.0125x, where x is in thousands ofphones produced, and the revenue represented by thousands of dollars is R=xp. Find theproduction level that will maximize revenue.arrow_forwardDecomposing Functions To join a book club, you pay an initial fee and then a fixed price each month for a book. The total cost in dollars of joining the club and buying n books is given by C=30+17n. What is the initial fee? What is the cost of each book after you are a club member?arrow_forward
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