Students may have trouble understanding how to account for time in the first question. They may benefit from writing the area after 1 day has passed, 2 days have passed, and so on. A table is a convenient way to gather this information.

Discuss why the area covered by mold is a function of the number of days that have passed. Attend explicitly to language that students learned in the prior unit on functions: The area of the mold, , is a function of the number of days, , since the mold was spotted, . The function, , expressing the mold relationship can be written as , where measures days since the mold was spotted, and gives the area covered by the mold in square millimeters.

Discuss whether a discrete graph or a curve is more appropriate and what domain would be suitable in this context. Ask questions such as:

• “Can the independent variable be something like 1.5, a number that is not a whole number? Is there an area that is associated with 1.5 days?” (Yes, some area of the bread is covered by mold at any point in time after . The mold doesn't disappear after being spotted and then reappear at exactly 1 full day, 2 full days, and so on.)
• “What would be the meaning of a point on the graph where the value of  is, for instance, between 2 and 3?” (It would mean the area covered by mold at some point more than 2 days but less than 3 days after mold was spotted.)
• “What domain would be appropriate for this function? Can the mold grow indefinitely?” (Since the area of the bread (the range) is limited, the exponential growth cannot continue indefinitely. By the end of one week, more than 1 square cm will be covered and, by the end of the second week, the values of the function will be close to or will exceed the total area of the bread.)

Students using paper and pencil may decide that it makes sense to connect the points on the graph but they will not yet know how to do so. Consider stating that they are connected (in a very specific way) and that their properties will be studied later.

Students using the digital version (or graphing technology along with the paper and pencil version) will see the continuous graph. If desired, you may want to demonstrate how using function notation to write the equation like can be put to use. Try typing or .

Students may confuse the terms "independent" and "dependent." Help them to think about which variable depends on the other in context.

Invite selected students to present their equations, making sure to indicate what each variable represents, as well as the units of the variable.

For the third question, point out that it is a short step from an equation for the area covered by the algae  to a similar equation with function notation. The equation gives the area covered by the algae at each time, , so a function, , can be defined using the same expression: , and .

Select students to share their graphs, the one created using the given horizontal and vertical boundaries, as well as the improved versions. Or display the graphs in the sample responses for all to see. Discuss questions such as:

• “Why were the given boundaries not good?” (The domain and range are both too wide. The range is so large that almost all the points look like they're about 0. It is even hard to tell what the starting value is.)
• “How can the context help us choose an appropriate graphing window?” (Negative values of time probably are not relevant because the amount of medicine in the body before the injection is likely insignificant or is not modeled by the equation. Large values of time (say ) are not likely important because the effects of the medicine after 100 hours are likely to be minimal.)

Graphing exponential functions can be challenging because they can increase or decrease very quickly. Emphasize that an appropriate graphing window can often be selected by using the context. Once the relevant domain of a function and the horizontal boundaries of a graph are chosen, the vertical boundaries can be selected based on the output values for that domain so that any meaningful trends (for example, exponential decay) are visible.