A rate of change on a graph tells you how much the output changes per unit of input. For a falling curve, read left to right to check that the amount decreases, then compare its steepness near the start and end to judge how fast it drops. A straight line has a constant rate; a curve that flattens does not.
Hints
- Hint 1
The horizontal axis counts hours, and the vertical axis measures milligrams. Read the curve from left to right as time passes. Does its height, which represents the amount of medicine, go up or down?
- Hint 2
The rate of change tells you how many milligrams the amount changes per hour. A steeper downward part loses more milligrams in an hour than a flatter part. Which part of the curve is steeper?
Step-by-step
Read the curve's direction and steepness
Step 1Find which way the amount changes
No Desmos needed. The graph already shows the curve. Read from left to right, since counts hours since the dose. The curve falls from at to at , so the amount of medicine decreases as time passes.
- Step 2
Use steepness to compare the speed of the decrease
Near , the curve drops steeply; farther right, it flattens. A steeper drop means more milligrams lost per hour, while a flatter drop means fewer lost per hour. So the medicine decreases rapidly at first and more slowly later. A constant rate would make a straight line, not this curve. Choice A.