2. The number P (t) of E. coli cells at time t (hours) in a petri dish is plotted in Figure 9. Calculate the average rate of change of P (t) over the time interval [1,3] and draw the corresponding secant line. 10,000- 8000- 6000- P(1) 4000- 2000 1000 10 2 3 FIGURE 9 Number of E. coli cells at time 3. The table below shows the temperature of water in a tub at time t, where W(t) is measured in degrees Fahrenheit and t is measured in minutes. At time t = 0, the temperature of the water is 55 F. The water is heated for 20 minutes, beginning at t = o. Values of W(t) at for selected times t are given in the table. t (minutes) 0 4 10 14 18 20 W(t) (degrees F) 55 60 67 75 80 85 Use the data from the table to find the following. Make sure you include units. a. What is the average rate of change of the temperature of the water on [0,20]? b. What is the average rate of change of the temperature of the water on [4,14]? t (hours) E(t) (hundreds) 0 2 5 8 0 4 13 21 23 4. The National Zoo sponsored a one-day contest to name a new baby panda. Zoo visitors deposited entries in a special box between noon (t = 0) and 8 P.M. (t = 8). The number of entries in the box t hours after noon is modeled by a differential function E for 0 st 8. Values of E(t), in hundreds of entries, at various times t are shown in the table above. Use the data in the table to approximate the average rate of change of entries, in hundreds of entries per hour, at which entries were being deposited between time t = 5 and t = 7. Show the computations that lead to your answer. 5. As an object in rectilinear motion moves, its distance s (in meters) from the origin after t seconds is given by s(t) = 2t3 + 4. Find the average velocity between t = 1 and t = 3. Use the mathematical definition of the derivative to find the derivative, f'(x), at any point on the curve. 6. f(x) = x-4x 7. f(x)=x+5 Use the mathematical definition of the derivative to find f'(x) at the indicated value of x. 8. f'(3) if f(x)=x+6 9. Find the equation of the tangent line to the graph of f(x) = x+5x at x=2. X-700/= 11/m X 874 =4 = 5-0 +0 Binocl=0]