Question 199·Easy·Nonlinear Functions
The graph shown gives the amount , in milligrams, of a certain medicine in a person's bloodstream as a function of the number of hours since the dose was taken.
Which choice best describes how quickly the amount of medicine in the bloodstream is decreasing over time?
For nonlinear-function graphs, use steepness to reason about rate of change: steep downward means fast decrease, and a curve that flattens means the decrease is slowing. Compare two time intervals on the graph to decide whether the rate is constant, speeding up, or slowing down.
Hints
Look at the steepness
Where the curve is steeper, the amount is changing more quickly.
Compare the left and right sides
Compare how much drops early (near ) versus later (near ).
Decide whether the rate is constant
If the graph were a straight line, the decrease would be at a constant rate. Is it a straight line here?
Desmos Guide
Use steepness to judge rate
In Desmos, remember that a steeper downward part of a curve means a faster decrease in as increases.
Compare changes over two intervals
Compare the drop in from about to versus from about to around . The much smaller drop later shows the decrease slows down over time.
Step-by-step Explanation
Connect steepness to rate of change
On a graph of amount vs. time, the steepness (slope) shows how quickly the amount is changing. A steeper downward curve means the amount is decreasing faster.
Compare early vs. later parts of the curve
From to about , the graph drops from about 200 mg to about 25 mg (a large decrease), but from about to it drops only from about 25 mg to about 10 mg (a much smaller decrease). So the amount decreases rapidly at first and then decreases more slowly as time goes on.