Don't just quote questions.  Tell me what you do know about the situation, and as best you can try to identify what you don't know.

Q:  What's the difference between finding a slope and finding a rate?

A:  It's a matter of interpretation.  If you are asked to find the rate of change of one quantity with respect to another, then you have to know what graph to find the slope of.  If you have a graph, you have to know just rate the slope represents.

Q:  How do I find the number of entire squares in a circle?

A:  A good sketch will give you a good idea.  But if you're dividing the circle into a lot of small squares, you have to get into the geometry of the circle, and of the square grid.  A lot of the geometry involved relies on the Pythagorean Theorem.  One important idea:  If the corner of the square furthest from the center is further than the radius, the square isn't entirely in the circle.

Q:  What do you mean by 'at what average rate does depth change with respect to clock time'.

A:  Here's an important definition:

The average rate of change of A with respect to B is (change in A) / (change in B).

So by this definition average rate of change of depth with respect to clock time must mean (change in depth) / (change in clock time).

Q:  Speed increases from 20 ft/sec to 30 ft/sec in 8 seconds.  So speed increases by 10 ft / second during the 8 seconds.  Would the distance therefore be 80 feet (10 ft / second * 8 seconds = 80 ft)?

A:  The speed is never less than 20 ft/sec, so you don't go less than 160 ft in 8 seconds.  An you don't go more than 240 ft (30 ft/sec for 8 sec is 240 ft).

So the distance is quite a bit greater that 80 ft.

It's not the difference in speeds that determines how far you go.  You can travel a long way at a steady 60 mph, with no change in speed.

It's the average speed that determines how far you can go. 

We don't know for sure how you get from 20 ft/s to 30 ft/s, but if we assume that the change is steady then the average would be 25 ft/s.  In 8 s, that would get you 200 ft, and that's probably the best estimate to start out with.

Similar question about water flowing at 10 gal/min, then a little later at 20 gal/min:  Our first estimate, without additional information, would be that the average rate is 15 gal/min.

Q:  How do you determine if your area estimates from a graph are high or low?

A:  Given a graph, look at how it curves.  Does it curve above or below the straight line segments that approximate it.

Q:  On an exponential graph, is there an average rate of change, or can it not exist?

A:  On an exponential graph, between any two points of the graph there is a change in y and a change in x.  The average rate of change of y with respect to x, for that interval, is just `dy / `dx.

Now think about a single point, and think about average rates of change over intervals that contain that point.  There are lots of possible intervals,