Question

Consider a ball rolling down the decreasing slope inside a semicircular bowl (the slope is steep at the top rim, gets less steep toward the bottom, and is zero (no slope) at the bottom). As the ball rolls from the rim downward toward the bottom, its rate of gaining speed

Answer 1

The answer would be:
It's rate of gaining speed decreases.
The rate at which speed changes is called acceleration, 
You can think of this problem as an inclined plane. But the angle of an inclined plane is constantly decreasing.
We know that on a frictionless inclined plane acceleration of an object is:
$a=gsin(\theta)$
Where g is the gravitational acceleration of the Earth and $\theta$ is the angle of an inclined plane. 
Using our analogy, the ball would start on an inclined plane with a 90-degree angle and that angle would continue to decrease to zero. 
The sine function is 1 at 90 degrees and is equal to zero at 0 degrees. Since our acceleration is proportional to the sine, and sine function is decreasing with the angle, our acceleration is also decreasing.