t(hours) 2 5 9 11 12
L(t) (cars per hour) 15 40 24 68 18
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 Z. Selected values of L(t) are given in the table above. Both E(t) and L(t) are measured in cars per hour, and time 7 is measured in hours after 5_AM.(t=0). Both functions are defined for 0≤ t≤ 12.
(a) What is the rate of change of E(t) at time t=7 ? Indicate units of measure.