ALCULUS Avon High School Name AP Calculus AB QUIZ 11 - Topics 4.1 & 4.3 Period Score _/ 10 Interpreting the Meaning of the Derivative & Rates of Change in Applied Contexts Part I. Multiple Choice Circle the best answer for each problem. Each problem is worth 2 points. You will need to use your TI-Nspire. 3.0 3.3 3.8 4.2 4.9 f(x 21.8 26.1 32.5 38.2 48.7 Some values of a differentiable function f are shown in the table above. What is the closest approximate value of f'(3.5)? (A) 8 (B) 10 (C) 13 (D) 16 2. The number of minutes of daylight during a day, L(t), at 40 North latitude is modeled by the function L(t) = 167.5sin 365 in 27 (t-80.75) + 731 where t is the number of days after the beginning of the year 2019. (Note: For January 1, 2019, t = 1; and for December 31, 2019, t = 365.) Which of the following is the correct interpretation of L'(364)? (A) The number of minutes of daylight is increasing by 1.760 minutes per day on December 30, 2019. (B) The rate at which the number of minutes of daylight is increasing by 0.469 minutes per day per day on December 30, 2019. (C) The number of minutes of daylight is increasing by 0.469 minutes per day on December 30, 2019. (D) The number of minutes of daylight is decreasing by 0.469 minutes per day on December 30, 2019. . Rock salt is being poured into a bin that is initially empty. During the work day, for 0 StS8 hours, the rock salt is being poured into the bin at a rate given modeled by S(t) = -3 4500 13 + 40 cubic meters per hour. After 1 hour, 1St 58, the rock salt is being removed from the bin at a rate modeled by R(t) = 24.925Jt cubic meters per hour. Which of the following best explains what S(5) - R(5) means in the context of the problem? (A) The rate at which the rock salt is leaving the bin is decreasing by 28.641 m'/hr a time t = 5 hours. (B) The amount of rock salt in the bin is decreasing by 28.641 m'/hr a time t = 5 hours. (C) The rate at which the rock salt is entering the bin is decreasing by 33.781 m'/hr a time t = 5 hours. (D) The amount of rock salt in the bin is approximately 28.641 m' when time t = 5 hours.Part II. Free Response You will need to use your TI-Nspire. Point values for each problem are given in ( ). Month 2 3 5 6 Temperature -8 50 72 88 F(1) The average daily maximum temperature, F(t), in F, for a certain city is shown in the table above. a. Use the data in the table to find the average rate of change of the maximum temperature from t= 1 to t = 6. Be sure to include the correct units. (Worth 1 point) b. Use the data in the table to estimate the rate of change of the maximum temperature at t = 4. Be sure to include the correct units. (Worth 1 point) c. The rate at which the maximum temperature changes for 1 1 5 6 is modeled by R(1) =4-2sin - -5 where R(t) is measured F /minute. Find R'(4) and explain what it means in the context of the problem using correct units. (Worth 2 points)