4.1 HW Student Copy

4.1 Interpretations of the Derivative in Context Homework 1. The temperature, ࠵ే࠵? , in degrees Fahrenheit, of a pizza placed on a serving dish is given by ࠵ే࠵? = ࠵౓࠵? ࠵ౡ࠵? , where ࠵ౡ࠵? is the time in minutes since the pizza was taken out of the oven. A. Is ࠵౓࠵? ′ ( ࠵ౡ࠵? ) positive or negative? Justify with a reason. B. What are the units of ࠵౓࠵? ′ (5) ? C. What is the meaning of ࠵౓࠵? ′ 5 = − 3 in context to the scenario? 2. The cost, ࠵శ࠵? (in dollars) to produce ࠵౔࠵? gallons of fresh-squeezed orange juice can be expressed as ࠵శ࠵? = ࠵౓࠵? ( ࠵౔࠵? ) . Using the proper units, explain the meaning of the following statements in terms of the orange juice. A. ࠵౓࠵? 500 = 2150 B. ࠵౓࠵? ′ 500 = 0.84 3. You have an inheritance of $100,000 from your grandparents, but you must invest the money in a mutual fund until you are 21 years old, that will pay an annual interest rate of ࠵౟࠵?࠵? compounded continuously. If you are 17 years old now, your balance, in dollars, can be defined as ࠵వ࠵? = ࠵ఴ࠵? ( ࠵౟࠵? ) . Interpret the following statements related to your inheritance, use the appropriate units. A. ࠵ఴ࠵? 7 ≈ 1323 0 B. ࠵ఴ࠵? ′ 7 ≈ 3307.50 © 2021 Jean Adams Flamingo Math.com 1 f t because the temperature will decrease afte being taken out of the oven degrees per min At t 5 mins the pizza's temperature will be decreasing at a rate of 3 degrees per min The cost to produce 500 gallons of orange juice is 2,150 After producing 500 gallons of orangejuice the rate of production is increasing 0.84 dollars per gallon If you invest 100,000 at a rate of 7 you will earn 13230 in 4 years You would earn 3307.50 per 1 rate for the 4 years of investing your inheritance at 7 per year

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 = ࠵ౘ࠵?࠵౔࠵? ࠵ౚ࠵? / ࠵ౠ࠵? 2 . Let ࠵హ࠵? = ࠵ౝ࠵? ( ℎ ) represent the force of pressure in Newtons, ࠵ౝ࠵? 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. ࠵ౝ࠵? 500 = 3.2 B. ࠵ౝ࠵? ′ 500 = 0.2 C. ࠵ౝ࠵? ′ ℎ = − 1 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 ࠵శ࠵? = ࠵౓࠵? ( ࠵౤࠵? ) . Describe the meaning of each quantity. A. ࠵౓࠵? 65 = 45 B. ࠵౓࠵? ′ 80 = 1.25 C. ࠵౓࠵? −1 200 ′ = 2.5 6. When a patient is prescribed an antibiotic to fight off infection, the dose, ࠵ష࠵? , in milligrams is a function of the patient’s weight, in pounds. Let ࠵ష࠵? = ࠵౓࠵? ( ࠵౤࠵? ) define the dosage. Interpret the meaning of each statement. A. ࠵౓࠵? 135 = 120 B. ࠵౓࠵? ′ 135 = 2.5 C. Estimate the dosage for a person weighing 140 pounds. © 2021 Jean Adams Flamingo Math.com 2 At 500 feet the astronauts experienced a g force of 3.29 After the astronauts surpass 500 the rate will increase at 0.2g per foot After the astronauts surpass h the rate will decrease at Ig per foot At a weight of 65lb it cost 45 to shred the documents After surpassing 80 lbs the cost of shredding increases by 1.25 per pop nd When 200 is spent on shredding the weight increases2.5 lbs per I dollar At a weight of 135lb the dosage is 120mg When you surpass the weight of 135 lbs the dosage increases by 2.5mg per lb 55 132.5mg