(1 point) Suppose the population P of rainbow trout in a fish hatchery is modeled by the differential equation dP = P P where P is measured in thousands of trout and t is measured in years. Suppose P(0) = 1. (a) How many trout are initially in the hatchery? 1 000 trout. (b) Find a formula for the population at any time. P(t) = 4/ ((3eA(4t))+1) thousands of trout. (c) What is the size of the trout population after a very long time? lim P0.) = thousands of trout. IPOO (1 point) R switch The figure above shows a circuit containing an electromotive force (a battery), a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Q). The voltage drop across the capacitor is Q/C, where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives Q RI+ = E r. C () Since the current is I = ddg, we have Rd_Q + Er Rd: CQ= () Suppose the resistance is 20 Q, the capacitance is 0.2F, a battery gives a constant voltage of E(t) = 30V, and the initial charge is Q(0) = Find the charge and the current at time t. Q= = I=