The differential equation in Example 3 of Section 2.1 is a well-known population model. Suppose the DE is changed to dP = P(aP - b), dt where a andb are positive constants. Discuss what happens to the population P as time t increases. as t increases. If Po > b/a, then P(t) as t increases; if 0 < Po < b/a, then P(t) -? Consider the following autonomous first-order differential equation. + 2) = y In(y + Find the critical points and phase portrait of the given differential equation. oF OF 0F -1-

Which set of reflections would carry trapezoid abcd onto itself? a) x-axis, y=x, y-axis, x-axis b) x-axis, y-axis, x-axis c) y=x, x-axis, x-axis d) y-axis, x-axis, y-axis, x-axis

Billy plotted −3 4 and −1 4 on a number line to determine that −3 4 is smaller than −1 4 .is he correct? explain why or why not

Ascientist wants to use a model to present the results of his detailed scientific investigation. why would a model be useful? a )because the model makes the concepts easier to understand b) because the model is easy to put together and to use c) because the model prevents other scientists from asking questions d) because the model requires the audience to pay full attention to it i don't know what to choose because between a and d a is much more likely than d because it only wants to get the attention of the audience. i'm confuse.