Transcript Predict the Growth Pattern

Predict the Growth Pattern
Swine Flu
Outbreak 2009
In 2009, the Swine Flu was
first reported on April 26,
2009.
The following data shows
how many cases were
reported each day in the
United States.
Determine an equation
to model the data.
Swine Flu Cases in the United States
Number of Confirmed Cases
180
160
140
120
100
80
60
40
20
0
0
1
2
3
4
Number of Days after 4/26
5
6
7
Swine Flu Cases in the United States
Number of Confirmed Cases
180
160
140
120
100
80
60
40
20
0
0
1
2
3
4
5
6
7
Number of Days after 4/26
How many cases do you expect to
be confirmed on the 8th day?
How close was your prediction?
Swine Flu Cases in the United States
Number of Confirmed Cases
250
200
150
100
50
0
0
1
2
3
4
5
Number of Days after 4/26
6
7
8
This is the graph 2 days later. How
do the additional data points change
your trendline?
Swine Flu Cases in the United States
Number of Confirmed Cases
450
400
350
300
250
200
150
100
50
0
0
2
4
6
Number of Days after 4/26
8
10
Swine Flu Cases in the United States
Number of Confirmed Cases
450
400
350
300
250
200
150
100
50
0
0
2
4
6
8
10
Number of Days after 4/26
How many cases do you expect to
be confirmed on day 10?
How close was your prediction?
Swine Flu Cases in the United States
Number of Confirmed Cases
700
600
500
400
300
200
100
0
0
2
4
6
8
Number of Days after 4/26
10
12
What is happening to the graph as
the number of days increases?
Swine Flu Cases in the United States
Number of Confirmed Cases
700
600
500
400
300
200
100
0
0
2
4
6
8
Number of Days after 4/26
10
12
Scientists use graphs to try to
estimate how many cases will arise
over time. In order to make a
prediction, they create graphs to try
to match the data. Your job will be to
help them determine which graph
will best predict the number of cases
nine days from now given the data
they have today.
Which graph do you believe
will best predict the number
of cases 9 days from now?
Swine Flu Cases in the US
Swine Flu Cases in the US
y = 28.1e0.3x
y = 65.0x - 107.8
1200
Number of Cases
Reported
Number of Cases
Reported
1000
800
600
400
200
1000
800
600
400
200
0
0
0
3
6
9
0
12
3
Swine Flu Cases in the US
9
12
9
12
Swine Flu Cases in the US
2
y = 0.6x 3 - 2.3x 2 + 17.9x + 24.7
y = 8.2x - 30.7x + 63.4
1000
1000
Number of Cases
Reported
Number of Cases
Reported
6
Number of Days after 4/26
Number of Days after 4/26
800
600
400
200
0
800
600
400
200
0
0
3
6
Number of Days after 4/26
9
12
0
3
6
Number of Days after 4/26
How was your prediction?
Swine Flu Cases in the US
Swine Flu Cases in the US
y = 28.1e
y = 65.0x - 107.8
Number of Cases
Reported
Number of Cases
Reported
4000
3000
2000
1000
15000
10000
5000
0
0
0
3
6
9
12
15
18
0
21
3
6
9
12
15
18
21
Number of Days after 4/26
Number of Days after 4/26
Swine Flu Cases in the US
Swine Flu Cases in the US
y = 0.6x 3 - 2.3x 2 + 17.9x + 24.7
y = 8.2x 2 - 30.7x + 63.4
6000
Number of Cases
Reported
5000
Number of Cases
Reported
0.3x
20000
5000
4000
3000
2000
1000
5000
4000
3000
2000
1000
0
0
0
3
6
9
12
15
Number of Days after 4/26
18
21
0
3
6
9
12
15
Number of Days after 4/26
18
21
Why do you suppose the linear
model is so inaccurate for
predicting in this case?
Swine Flu Cases in the US
Swine Flu Cases in the US
y = 28.1e
y = 65.0x - 107.8
Number of Cases
Reported
Number of Cases
Reported
4000
3000
2000
1000
15000
10000
5000
0
0
0
3
6
9
12
15
18
0
21
3
6
9
12
15
18
21
Number of Days after 4/26
Number of Days after 4/26
Swine Flu Cases in the US
Swine Flu Cases in the US
y = 0.6x 3 - 2.3x 2 + 17.9x + 24.7
y = 8.2x 2 - 30.7x + 63.4
6000
Number of Cases
Reported
5000
Number of Cases
Reported
0.3x
20000
5000
4000
3000
2000
1000
5000
4000
3000
2000
1000
0
0
0
3
6
9
12
15
Number of Days after 4/26
18
21
0
3
6
9
12
15
Number of Days after 4/26
18
21
What about the equation
y = 0.6x3 – 2.3x2 + 17.9x + 24.7
might make this graph the most
accurate ?
Swine Flu Cases in the US
y = 0.6x 3 - 2.3x 2 + 17.9x + 24.7
Number of Cases
Reported
6000
5000
4000
3000
2000
1000
0
0
3
6
9
12
15
Number of Days after 4/26
18
21