The rate at which cars enter a parking lot is modeled by E(t)=30+5(t-2)(t-5)e^-0.2t. The rate at which cars leave the parking lot is modeled by the differentiable function L. Selected values of L(t) are given in the table below. Both E(t) and L(t) are measured in cars per hour, and time t is measured in hours after 5 AM. (t=0) Both functions are defined for 0≤t≤12. a) How many cars enter the parking lot from time t=0 to time t=12?
b) Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate ( ∫upper 12 lower 2 ) L(t)=dt. Using correct units, explain the meaning of ( ∫upper 12 lower 2 ) L(t)=dt in the context of this problem.
d) For 0≤t≤6, 5 dollars are collected from each car entering the parking lot. For 6≤t≤12, 8 dollars are collected from each car entering. How many dollars from time t=0 to t=12?