A large vat is initially filled with a saltwater solution. A solution with a higher concentration of salt flows into the vat, and the solution flows out of the vat at the same rate. The number of pounds of salt in the vat at timer minutes is modeled by the function A that satisfies the differential equation 4 = 6- 0.02A. At time t= 10 minutes, the vat contains 50 pounds of salt. a) Write an equation for the tangent line to the graph of A at t = 10. Use the tangent line to approximate the number of pounds of salt in the vat at time = 12 minutes. b) Show that A(t) = 300-250e2-0.02 satisfies the differential equation=6 -0.02A with initial condition A(10) = 50. c) The flow of the solution into the vat is stopped, and the solution is drained. The depth of the solution in the vat is modeled by the function h that satisfies the differential equation- measured in meters, r is the number of minutes since draining began, and k is a constant. If the depth of the solution is 16 meters at time r =0 minutes and 4 meters at time r-30 minutes, what is h(t) in terms 4h =-kh, where hir) is dt of 1?