Download Day 3_ ELP Exponential ARW and Rebound TI nspire Verion

ELP Lesson Plan: Exponential
At the end of the day students will…
Calculate the exponential rule and determine the equation from a table and a story
Be able to create an exponential equation from a table
Standards Taught
Identify exponential patterns
Anticipation of next steps…
Solving exponential equations using the table and graph on the calculator
Warm-Up…
Scientific notation, Percent increase and decrease
Consider the following two tables and work with students to find the rule:
Key Question: What do you have to multiply each value in the chart by to get the next
value? How do you go up the table?
x
y
x
y
0
2.567
0
12
1
2.6183
1
12.672
2
2.6707
2
13.382
3
2.7241
3
14.131
4
2.7786
4
14.922
5
5
Step by Step Instruction…
Bounce exponential worksheet (This worksheet is entirely made up of perfect tables or nearly
perfect tables, students will try to write equations from the y-intercept and so they should walk
the nearly perfect tables back to 0) Next they will learn to write exponential equations from
anywhere on the table and finally from skipping tables
Independent Practice…
Worksheet
Rebound!
If a ball is dropped from a height of 50 inches and it is allowed to bounce 4 times,
what will the height of the ball be after the 4th bounce?
Part I – The experiment
Step 1: Drop a ball from 50 inches above the ground and record the height of the ball
after the first bounce.
# bounces
Height of Ball
(Inches)
0
50
1
Step 2: Based on the data you collected above predict the height of the ball after the 4th
bounce, if the ball were dropped from an initial height of 50 inches. Show your work in
the space provided. You should use a graph, table and/or equation to justify your
prediction.
Step 3: Now drop the ball from a height of 50 inches and record the height of the ball
after the 4th bounce.
Height after 4th bounce______________________
Step 4: How accurate was your prediction?
Step 5: If something went wrong what do you think might have caused it?
Step 6: Initially you dropped the ball and allowed it to bounce only one time. What can
be done to improve the experiment?
Step 7: Let’s go back to the data collection process that we started at the beginning of this
investigation. This time we will allow the ball to bounce more than one time and record
the height after each bounce.
# bounces
Height of Ball
(Inches)
0
50
1
2
3
Graph the data: (always include labels and a title)
Does this data represent a function?
How do you know?
What shape does the data form?
As you probably noticed, although the height of the ball after a given bounce is a function of
the number of the bounces, it is called exponential.
Each time the ball bounces it rebounds to a fraction of its previous height. The bouncier
the ball the higher this fraction is! Exponential functions are characterized by repeated
multiplication.
The chart below represents the relationship between the number of bounces of a “not-sobouncy” ball and its height after each bounce. Enter the data into a Lists and Spreadsheets
document so we can later test the equation(s) you develop to model the data. We’ll use
this data to explore the idea of an exponential function because the pattern is easily
discovered.
# bounces
Height of Ball
(Inches)
0
50
1
25
2
12.5
3
6.25
4
5
Hmmm. What’s
happening to the height of
the ball after each
bounce?
3.125
1.5625
Take a moment to examine and analyze this chart and in your own words explain the
relationship.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
Tell the story through an equation!
Remember that the shortcut for repeated multiplication is an exponent. Work with
your neighbor to make a function equation that generates the data in the above table.
You can verify that you have the correct equation by checking it on your calculator.
Exponential functions are characterized by a starting value and a constant multiplier. It is
a process of repeated multiplication. Come up with the exponential function equation that
represents your bouncy ball and use this equation to predict the height of the ball after
the 4th bounce when it is dropped from an initial height of 100 inches. Have fun and
don’t get hurt.
Name:
Period:
Date:
Exponential
Find the exponential equation from the following table of values:
x
y
x
y
x
y
0
1
0
2.3
1
3
1
2.5
1
2.65
2
8.1
2
6.25
2
3.04
3
21.87
3
15.625
3
3.5
4
59.05
4
39.063
4
4.02
5
159.43
Equation
Equation:
Equation:
x
y
x
y
x
y
-2
-2.2
-5
5
2
14
-1
-2.42
-4
8
3
49
0
-2.66
-3
12.8
4
171.5
1
-2.93
-2
20.48
5
600.25
2
-3.22
-1
32.768
6
2100.9
6
Equation:
0
Equation:
10
Equation:
Make a table from the following scenarios and then write the exponential equation.
Label each row in the shaded region.
In 1982, Bob puts $10000 in the stock market and was earning 6.3% interest on his
investment.
Equation:
If Bob continued to earn this interest rate, how much would his investment be worth in
2012?
The population of Billings South Dakota is increasing at a rate of 25% per year in the mid
70’s. The population of Billings was 72,000 in 1975.
Equation:
If Billings continued to grow at this rate what will the population be in 2012?
Sales at Billy’s Car Wash are increasing 3.2% per year. Sales were $125,000 in 1998.
Equation: