7c. How would you describe the rate of increase of the function?
As increases, the function increases at a
faster and faster rate.
As increases, the function increases at a
slower and slower rate.

The rate of increase of a function can often be determined by looking at its derivative. If the derivative is increasing, it means the function itself is accelerating, and you’re right; it’s increasing at a faster and faster rate! Conversely, if the derivative is decreasing, then the function’s growth is slowing down. Visualizing this with graphs helps—seeing how steep the curve gets can paint a clearer picture of the growth behavior!

In real life, the concept of a function’s rate of increase can be found all around us! For example, consider a bank account with compound interest. Initially, the rate of increase (or the amount earned) may seem modest, but as time goes on, interest is earned not just on the initial amount but also on the interest already accrued, making the growth seem faster—just like an accelerating function!