Chemical Reactions When certain kinds of chemicals are combined, the rate at which t...

Chemical Reactions When certain kinds of chemicals are combined, the rate at which the new compound is formed is modeled by the autonomous differential equation

where k > 0 is a constant of proportionality and Here X(t) denotes the number of grams of the new compound formed in time t.

(a) Use a phase portrait of the differential equation to predict the behavior of

(b) Consider the case when Use a phase portrait of the differential equation to predict the behavior of X(t) as

(c) Verify that an explicit solution of the DE in the case when k = 1 and Find a solution that satisfies Then find a solution that satisfies Graph these two solutions. Does the behavior of the solutions as agree with your answers to part (b)?