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e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?

e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...
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Answer only option e. Please try not to use derivatives or integrals to calculate the stuff. Thank you.
Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. a. What does it mean to say that C(2000) = 800? b. What are the units of C'(r)? c. Suppose that C(2000) = 800 and C'(2000) = 0.35. Estimate C(2100), and justify your estimate by writing at least one sentence that explains your thinking. d. Do you think C'(2000) is less than, equal to, or greater than C'(3000)? Why? e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?
Transcribed Image Text:Activity 1.5.3. A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. a. What does it mean to say that C(2000) = 800? b. What are the units of C'(r)? c. Suppose that C(2000) = 800 and C'(2000) = 0.35. Estimate C(2100), and justify your estimate by writing at least one sentence that explains your thinking. d. Do you think C'(2000) is less than, equal to, or greater than C'(3000)? Why? e. Suppose someone claims that C'(5000) = -0.1. What would the practical mean- ing of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?
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