Transcript Alg 1 - 11.4
11-4 Linear, Quadratic, and Exponential Models Warm Up 1.
Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24).
The population of a town is decreasing at a rate of 1.8% per year. In 1990, there were 4600 people. 2.
Write an exponential decay function to model this situation.
y = 4600(0.982)
t
3.
Find the population in 2010.
3199
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
Learning Targets
Students will be able to: the function. Compare linear, quadratic, and exponential models and given a set of data, decide which type of function models the data and write an equation to describe
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
Look at the tables and graphs below. The data show three ways you have learned that variable quantities can be related. The relationships shown are linear, quadratic, and exponential.
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
Look at the tables and graphs below. The data show three ways you have learned that variable quantities can be related. The relationships shown are linear, quadratic, and exponential.
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
Look at the tables and graphs below. The data show three ways you have learned that variable quantities can be related. The relationships shown are linear, quadratic, and exponential.
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
In the real world, people often gather data and then must decide what kind of relationship (if any) they think best describes their data.
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models Graph each data set. Which kind of model best describes the data?
Boxes Reams of paper 1 10 5 50 20 50
x
–3 –2 0 1 2 3
y
0.30
0.44
1 1.5
2.25
3.38
200 500 Time(h) Bacteria 0 1 2 3 4 24 96 384 1536 6144
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
Another way to decide which kind of relationship (if any) best describes a data set is to use patterns.
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models Look for a pattern in each data set to determine which kind of model best describes the data.
Height of golf ball Time (s) Height (ft) 0 1 2 3 4 4 68 100 100 68
Money in CD Time (yr) Amount ($) 0 1 2 3 1000.00
1169.86
1368.67
1601.04
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models Data (1) –2 –1 0 1 2 Data (2) 10 1 –2 1 10 Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models
After deciding which model best fits the data, you can write a function. Recall the general forms of linear, quadratic, and exponential functions.
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models Use the data in the table to describe how the number of people changes. Then write a function that models the data. Use your function to predict the number of people who received the e-mail after one week.
Time (Days) 0 1 2 3 E-mail forwarding Number of People Who Received the E-mail 8 56 392 2744
f
Exponential
x
7
Holt Algebra 1
11-4 Linear, Quadratic, and Exponential Models Remember!
When the independent variable changes by a constant amount, • linear functions have constant first differences.
• quadratic functions have constant second differences.
• exponential functions have a constant ratio.
HW pp. 793-795/8-19,23-39,32-40
Holt Algebra 1