Answer the following question.

1.

A pond initially contains 6,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.04 grams of this chemical per gallon flows into the pond at a rate of 200 gal/ h. The mixture ows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniforme distributed throughout the pond. (a) Write a differential equation for the Mount of chemical in the pond at any time. Let q(t) denote the amount of chemical in the pond at time t. NOTE: Use q as aft). dq gram. 5 _ hour (h) Hear much of the chemical will be in the pend after a very long time? Does this limiting amount depend on the amount that was present initially? q = grams The limiting amount depend on the amount that was present initially. Solve each of the following initial value problems. Describe in a few 1words how the solutions resemble, and differ from each other. dy_ _ (a) E _4y_3, M0) ya (13) E = 2y - 8, 9(0) = yo 0! (C) (T: = 2:9 - 16, 1:03) = ya Choose one v If y.) = 15,r then the solution of the initial value problem (o) is the largest one for large positive 15. If m = 15, then the solution of the initial value problem (a) is the largest one for large positive t. If m = 15, then the solution of the initial value problem (13) is the largest one for large positive t. Determine the order of the given differential equation and state whether the equation is linear or nonlinear. 6151: d4} day dy + + + + = 20 (35 (14 c113 cit y This equation is v . The order of the equation is I: A Determine the order of the given differential equation and state whether the equation is linear or nonlinear. This equation I' J \"near nonlinear