10. A zoo sponsored a one-day contest to name a new baby elephant. Zoo visitors deposited entries in a special box between noon (t =0) and 8 P.M. (1=8) . The number of entries in the box t hours after noon is modeled by a differentiable function E for 0 St 8. Values of E (t) , in hundreds of entries, at various times t are shown in the table below. (hours) 2 E(t) (hundreds of 0 13 21 23 entries) a. Use the data in the table to approximate the rate, E' (t) , at which entries were being deposited at t = 6. Show the computations that lead to your answer. Indicate units of measure. b. At t =6 there are 800 entries in the box. Use your answer from part a to approximate the equation of the tangent line to E (t) at t = 6. c. Use your tangent line equation from part b to approximate E(7)