There are 3 parts:

Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point. Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f (a ) is a real number. A large vat is initially filled with a saltwater solution. A solution with a higher concentration of salt flows into the vat, and solution flows out of the vat at the same rate. The number of pounds of salt in the vat at time t minutes is modeled by the function A that satisfies the differential equation d A dt = 6 - 0.02A. At time t = 10 minutes, the vat contains 50 pounds of salt. (a) Write an equation for the line tangent 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 t = 12 minutes. (b) Show that A (t) = 300 - 250e0.2-0.02 satisfies the differential equation d A dt =6 - 0.02 A with initial condition A (10) = 50. (c) The flow of solution into the vat is stopped, and the solution is drained. The depth of solution in the vat is modeled by the function h that satisfies the differential equation -= -KVh, where h (t) is measured in meters, t is the number of minutes since draining began, and & is a constant. If the depth of the solution is 16 meters at time t = 0 minutes and 4 meters at time t = 30 minutes, what is h (t) in terms of t