A company manufactures rope, and the total cost of producing r r feet of rope is C ( r ) C(r) dollars. What does it mean to say that C ( 2000 ) = 800 ? C(2000)=800? What are the units of C ′ ( r ) ? C′(r)? Suppose that C ( 2000 ) = 800 C(2000)=800 and C ′ ( 2000 ) = 0.35 . C′(2000)=0.35. Estimate C ( 2100 ) , C(2100), and justify your estimate by writing at least one sentence that explains your thinking. Do you think C ′ ( 2000 ) C′(2000) is less than, equal to, or greater than C ′ ( 3000 ) ? C′(3000)? Why? Suppose someone claims that C ′ ( 5000 ) = − 0.1 . C′(5000)=−0.1. What would the practical meaning of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?

Suppose the government decides to issue a new savings bond that is guaranteed to double in value if you hold it for 20 years. assume you purchase a bond that costs $25. a. what is the exact rate of return you would earn if you held the bond for 20 years until it doubled in value? (do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. if you purchased the bond for $25 in 2017 at the then current interest rate of .27 percent year, how much would the bond be worth in 2027? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) c. in 2027, instead of cashing in the bond for its then current value, you decide to hold the bond until it doubles in face value in 2037. what annual rate of return will you earn over the last 10 years? (do not