Choose and interpret the scale of a graph to appropriately represent an exponential function.

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Presentation transcript:

Choose and interpret the scale of a graph to appropriately represent an exponential function.

Learning Goal 2 (HS.N-Q.A.1, 2, 3): The student will be able to use units to solve multi-step contextual problems.

 Darryl lives on the third floor of his apartment building. His bike is locked up outside on the ground floor. At 3:00p.m., he leaves to go run errands, but as he is walking down the stairs, he realizes he forget his wallet.  He goes back up the stairs to get it and then leaves again.  As he tries to unlock his bike, he realizes that he forgot his keys. One last time, he goes back up the stairs to get his keys.  Then he unlocks his bike. He is on his way at 3:10pm.

 The video shows bacteria doubling every second.  After watching the video through once, we will go through it slowly.  You will need to make a t-chart showing how many bacteria there are at 0, 1, 2, 3, 4 seconds.

Time (sec) Number of Bacteria Graph the data you have in your t-chart.

 At time 0 seconds, there are 2 bacteria, and the number of bacteria in the Petri dish doubles every second.  **This doesn’t describe the EXACT number of bacteria at a given time in the video but it is a reasonable estimate.**  Assignment: ◦ Add to your graph an amount that represents the bacterial population growth beyond the 6-second mark.  What challenges are you running into?

 What will the shape of the graph be after the 6- second mark?  Will the curve be perfectly vertical?

 The narrator in the video stated, “Just one bacterium, dividing every 20 minutes…”  If one bacterium divides once every 20 minutes, how much “real time” is passed in what we watched in the time- lapse video?  Re-watch the video:

 One second of video time equal 20 minutes of real time.  How does this effect our table?  How does this effect our graph?  Make these adjustments to your table and graph. Extend your data for up to five hours (300 minutes).

Time (min)Number of Bacteria , , , , , , ,536 We could also change the horizontal axis to hours. These units would be more appropriate.

 The graph of the count of bacteria is an example of a graph of an exponential function.  What is the difference between a linear graph and an exponential graph?