Lesson 3.notebook
September 15, 2015
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Lesson 2 Homework: Graphs of Quadratic Functions
1. Here is an elevation versus time graph of a ball rolling down a ramp. The first section of the graph is slightly curved.
a. From the time of about 1.7 seconds onwards, the graph is a flat horizontal line. If Ken puts his foot on the ball at time 2 seconds to stop the ball from rolling, how will this graph of elevation versus time change? 2. Use the table below to answer the following questions.
a. Plot the points (x,y) in the table on the graph (except when x = 5)
b. The y‐values in the table follow a regular pattern that can be discovered by computing the differences of the consecutive y‐values. Fund the pattern and find the y‐value when x = 5.
b. Estimate the number of inches of change in elevation of the ball from 0 seconds to 0.5 seconds. Also estimate the change in elevation of the ball from 1.0 seconds to 1.5 seconds.
c. Plot the point you found in part (b). Draw a curve through the points in your graph. Does the graph go through the point you plotted?
c. At what point is the speed of the ball the fastest, near the top of the ramp at the beginning of its journey or near the bottom of the ramp? How does your answer to part (b) support what you say?
Lesson 3: Graphs of Exponential Functions Find your seat!
Student Outcomes:
Please remember to bring in your Box of TISSUES
§ Students choose and interpret the scale on a graph to appropriately represent an exponential function. Students plot points representing number of bacteria over time, given that bacteria grow by a constant factor over evenly spaced time intervals.
Lesson 3.notebook
September 15, 2015
Example 1 : The story: Sketch a graph that depicts Darryl lives on the third floor of his apartment building. His bike is Darryl’s change locked up outside on the ground in elevation floor. At 3:00 p.m., he leaves to go run
over time. errands, but as he is walking down the stairs, he realizes he forgot 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. He then unlocks his bike, and he is on his way at 3:10 p.m. Example 2‐ Watch the following graphing story: The video shows bacteria doubling every second. Create a chart for the time frames of 0 to 6 seconds
Time 1
3
0
2
4
# of Bacteria
Graph and compare with the first graph!
5
6
Lesson 3.notebook
A few questions: • Will the curve ever be perfectly vertical? • Is our graph "Real time" or better yet how long does it take for one bacterium to divide? • What column could we add to our table?
• How can we change our existing graph?
This type of graph is called an exponential function! Here is our last example with a slight difference? What is the difference??
September 15, 2015
Let's now extend the graph for a five hour time frame! Remember we are estimating!
Assume that a bacteria population doubles every hour. Which of the following three tables of data, with x representing time in hours and y the count of bacteria, could represent the bacteria population with respect to time? Lesson 3.notebook
Closing: List some facts about the following three types of graphs.
LINEAR
QUADRATIC EXPONENTIAL
September 15, 2015
Problem set #2
Attachments
Bacteria video CW example 2