Drag the corresponding term or set of units to the phrases. Then complete the table on the next slide. 1. instantaneous rate of change of position 2. possible units of acceleration 3. units for instantaneous rate of change of volume, V()) , where is measured in gallons and / is measured in hours c A. velocity C. gallons per hour per 4. possible units for position hour D. meters F. meters per second per second 5. instantaneous rate of change of velocity B. acceleration E. meters per second 6. possible units for velocity G. gallons per hour 7. units for instantaneous rate of change R(), R is measure in gallons per hour and ris measured in hours.Instantaneous Rate of Change Average Rate of Change 6. When t =7 hours 4. During the first five minutes 1. Over the time interval from t = 2 to t = 5 3. At noon 5. Over the twelve hour time period 2. After three seconds have elapsedComplete each of the following verbal descriptions by lling in the blanks with the information that is missing. Be sure to include appropriate units. The rst one is completed for you as an example. Example: Um gives the volume of water in a tank in liters after t minutes. wait = 20 means that after _. there are 20 liters of water in the tank. V13) = -2 means that . the volume of water in the tank is at a rate of 2 liters per minute . 1. A(t) gives the area of the surface of an oil slick, in square kilometers (km2) after t hours. A(24) = 17 means that after the area of the surface of the oil slick is A'(5) = 4 means that when have elapsed, the area of the surface of the oil slick is at a rate of 2. C(x) gives the cost in dollars of digging a hole x feet deep. C(20) = 140 means that it costs to dig a hole that is deep. C'(20) =5 means that when the hole is the cost of digging is at a rate ofam gives the acceleration in cmrsec2 after 1? seconds. 3(2) = 6 means that after :I the acceleration is |:|. 21?): 3 means that after :I the acceleration is Pm gives the population of population. in billions of people, of the world tyears after 1950. P(4UJ=5.3 means that in the year I:, r3160) = 0.0?3 means that Rm gives the rate, in pints per second. that oil is owing into a tank after tseoonds. R\" D} = 3 means that R16} = 412 means that Z Activity #4 The instantaneous rate of change of a function fwilh respect to its independent variable x at the instant when x = a is determined by computing r'ia). It is always important to read each and every word in a math problem. Mathematicians tend not to throw in lots of extra words. so usually, every word is important. Read the two questions carefully, and then do the following for each: a} Decide which of the two calculations indicated is the appropriate one to answer the question. Place a check mark in the appropriate box. b) Verity both calculations. using your calculator. Remember that you can use the numerical derivative capability on a graphing calculator to compute a derivative of a function at a point. c) Provide correct units for both calculations. 1. Water is flowing into a tank so that the volume of water in the tank, in liters, after t seconds is given by the function V(t) =74 -9e-03 . At what rate is the amount of water in the tank increasing after 15 seconds? O V(15) = 73.900 O V'(15) = 0.030 units: units: 2. Oil is being siphoned out of a tank at a rate of S(t) =5-vt gallons per hour where t is measured in hours and Ost $ 5. At what rate is oil being siphoned out of the tank after 2.4 hours have elapsed? O S(2.4) = 3.451 S'(2.4) =-.323 units: units