Students may find it challenging to choose a scale for the axes in a way that helps them plot the points and see a pattern. If they are still struggling to choose a scale for the axes after a few minutes, ask students to think about the greatest and least vertical coordinates they need to show on the graph and what the height of each rectangle on the grid should be to show these values. In addition, if they get stuck plotting points, suggest that they first make a table of values.

Make sure that students understand that a growth factor that is between 0 and 1 causes the value to decrease each time the factor is applied. Tell students that the quantity changes exponentially, though sometimes people use the more specific terms exponential growth and exponential decay to indicate whether the amount is increasing or decreasing. The multiplier is still called the growth factor, but when it is a positive number less than 1, the result decreases with every iteration. Sometimes people use decay factor to indicate that a quantity that decreases exponentially involves a positive factor that is less than 1, but it is still correct to use the term "growth factor."

Discuss questions such as:

• “What is the growth factor for this situation?” ()
• “When the growth factor is between 0 and 1, what do you expect to happen to the -values of points on the graph as you read from left to right? Explain your reasoning.” (I expect the values to decrease as they get closer and closer to the -axis. This happens because the -values are being multiplied by a fraction that is between 0 and 1, which decreases its value while still being positive.)

Time permitting, consider discussing:

• “What does a value of 2.5 mean?” (A value of 2.5 means 2.5 weeks or a little more than 17 days after treatment begins.)
• “How did you estimate the area covered by algae after a certain non-whole-number of weeks?” (We can use the graph to estimate the area of algae, which is between the area in week 2 and that in week 3, though not too much precision can be given. It is definitely less than 27 square yards and more than 9 square yards. Following the general trend of the points decreasing less and less rapidly as time goes on, an estimate of 15 is reasonable.)
• “Someone says that after seven weeks, the algae will disappear. Do you agree?” (No, if we keep multiplying by , the area will keep getting smaller, but never reach 0. No, after seven weeks there would be about of a square yard or 1 square foot covered by algae. Yes, rounded to the nearest square yard, there are 0 square yards covered by the algae after seven weeks.)

If students are unsure if or of the luminescence stays each hour, consider asking:

• “Tell me more about how much luminescence stays and how much goes away.”
• “Is the graph showing the luminescence that stays or the luminescence that goes away?”

The goal of this discussion is to highlight the connections between the equation, the graph, and the quantities in the situation. Ask students:

• “How can we use an equation to express the luminescence of the glow stick () after hours using an equation?” ( )
• “Where can we see the 9 lumens in the graph?” (the vertical intercept)
• “What about the ?” (The coordinates tell us that the brightness reduces by of the previous luminescence each hour, so of it, which is most of it, is left every hour.)

Also consider asking:

• “Will there be any luminescence remaining from the glow stick 12 hours after it starts glowing?”
• “If so, when will the glow stick stop glowing?”

These are difficult questions to answer. The mathematical model will never reach 0 because a positive quantity multiplied by is always positive. Practically speaking, however, the chemical reaction causing the glow stick to luminesce will end, unless more chemicals are added to the situation. This is a good opportunity to remind students that mathematical models are simplified descriptions of reality.