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This document contains practice problems and solutions related to interpretations of the derivative in a context homework assignment. Topics include temperature changes of a pizza, costs to produce orange juice, inheritance investments, and antibiotic dosages.

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4. The Apollo 11 Crew left Earth for the moon on July 16, 1969, at 9:32 a.m. in a Saturn V rocket. They experienced forces of about 1.2g at liftoff and reached a maximum force of about 3.9g. The g-force is measured in Newtons defined as 1N = kg(m/s 2 ). Let F = p(h) represent the force of...

4. The Apollo 11 Crew left Earth for the moon on July 16, 1969, at 9:32 a.m. in a Saturn V rocket. They experienced forces of about 1.2g at liftoff and reached a maximum force of about 3.9g. The g-force is measured in Newtons defined as 1N = kg(m/s 2 ). Let F = p(h) represent the force of pressure in Newtons, p on the astronauts at a height h, in meters. Explain what each of the following quantities mean in relation to the astronauts. Give units for the quantities in Newtons. A. p(500) = 3.2 Wh the roc.ket was 500 meters (ll'.X)Ve 1'he taut"\chpnd, e -force was 3. New-tones B. p' (500) = 0.2 A re.a if':j_ 500 m high, the. -forte_ on e crew lS I nCieas,(\9 at o.. re1.te of o. Newtoris pe.r meter, C. p'(h) = -1 Toics 1s the nei9ht1 h, in meters> here_ -lhe rQ-te. of the force of' +he. crew ,s decrec.61 o± o.. nrle of 1 New-rot'\ per meter. 5. A law firm pays a third-party to pick up confidential documents and deliver them to a shredding service. This cost, C, in dollars, is a function of the weight of paper, w, in pounds, that is shredded for each client's case, such that C = f (w). Describe the meaning of each quantity. A. f(65) = 45 The eost to 5 hrw 4.,5-1 bs (:)-t paper IS $4-S: s. rcso) = 1.2s After s hredd inoj 80- lbs of pa.perj the. mte +o Sr1f'ed rl-lb. oadit,o)'lQ.I paplf is if\Cfet:lSl a;t $ t.. 3-5 per ptbunc.L C. [f- c200)]' = 2.5 WneA xou s d o Of' SYlredd.i , it 1 to.k5..s f bi of pa.per before the cost of S hreddi09 i ()e£ea5es b $!.OD 6. When a patient is prescribed an antibiotic to fight off infection, the dose, D, in milligrams is a function of the patient's weight, in pounds. Let D = f(w) define the dosage. Interpret the meaning of each statement. A. 1 c135) = 120 A pa.t4ef\+ w})o weighs / 35 _I b n eds J rn i 11 ,·gV"'a.ms of fhe anti b r o+r c. B. ['(135) = 2.5 The rare of' antibiotic -fur (A, f)

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