Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t=50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If ne swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MPy) is MPy = (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the character.)

Principles of Economics 2e
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ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
ChapterA: The Use Of Mathematics In Principles Of Economics
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Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is
t = 50+8e-0.00005y
Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If
he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he
will win the meet.
Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards?
Ben's marginal productivity of swim time given y practice yards (MP) is
(Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^
MPy
character.)
Transcribed Image Text:Ben's swim coach estimates that his time, t, in the 100-yard butterfly at a big upcoming meet as a function of the number of yards he swims per week, y, is t = 50+8e-0.00005y Based on this production function, his coach also estimates that if Ben swims 20,000 yards per week, his time will be 52.94 seconds, and he will finish tenth place. If he swims 40,000 yards per week, his time will be 51.08 seconds, and he will come in third. If he swims 60,000 yards per week, his time will be 50.40 seconds, and he will win the meet. Use calculus to determine Ben's marginal productivity of time given the number of yards he practices. Is there diminishing marginal productivity of practice yards? Ben's marginal productivity of swim time given y practice yards (MP) is (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ MPy character.)
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