1. If the doubling pattern continues, how many square millimeters will the mold cover 4 days after she noticed the mold? Be prepared to show your reasoning.

Compare your answer:

16 square millimeters. $2·2·2·2$ or $2^4$ is 16.

2. Represent the relationship between the area $A$, in square millimeters, covered by the mold and the number of days $d$ since the mold was spotted using:

a. A table of values, showing the values from the day the mold was spotted through 5 days later.

b. An equation

c. A graph

Compare your answers:

1. Number of days, $d$	Area, $A$, in sq mm
   0	1
   1	2
   2	4
   3	8
   4	16
   5	32

2. Equation: $A=1·2^d$ or equivalent (like $A=2^d$ ).
3. Your graph may be discrete or continuous, this example is a discrete graph.

3. Discuss with your partner: Is the relationship between the area covered by mold and the number of days a function? If so, write ____ is a function of ____. If not, explain why it is not.

Compare your answer:

Yes.

• The area covered by mold is a function of the number of days that have passed. At any given time since mold was spotted, there is a certain area of the bread that is covered in mold.
• The number of days that have passed is a function of the area covered by the mold up to a certain point (e.g., when the entire piece of bread is already completely covered, the area of mold would correspond to more than one day). We do not have a way to write this relationship using an equation, but we could use a table or a graph to show the relationship.