Algebra II Pre AP
Notes 12.3 – Using Models to Make Predictions
HW: Textbook Pg. 525 (7 – 14)
1. The manager of a band has been testing various prices for song downloads. He randomly selects a sample of
weeks from the previous year and records the price and the number of downloads sold that week. The table
shows his data.
a) What is a model for the data using regression?
Linear R 2  .793
Quadratic
R 2  .909
Exponential R 2  .955
Exponential Model would be the best regression for the data until you try to make a judgement as to pricing.
b) On average, it costs the band $4000 to produce and record a song. The band needs to decide on the price
to charge for a song download. Make a judgment on the data to decide how to price the song. Explain
your reasoning.
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
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Between $.69 - $.79 just viewing the data points collected.
According to the linear model, they can break even at $.74. Although the exponential model fit the data
and the situation better, there was no price value that would earn them $4000 or more.
Since the exponential regression would be the better predictor they would not be able to make any
money (actually lose money) based on the prices and the number of downloads associated with those
prices .
2. The health department for a major city recorded data of the spread of an infectious disease. The table shows the
number of new cases reported per 100,000 people for the select days. The first case was reported on Day 0.
a) What is the best regression model for this data?
Linear R 2  .0187
Quadratic
R 2  .840
Exponential R 2  .0839
Quadratic Regression y  .342 x 2  20.923x  66.963
b) The same disease is starting in a city with a population of 1.82 million. On average, 8% of new cases
require care at a hospital. Hospitals in this city must decide how many new patients they need to prepare
for. Make a judgment based on the model to decide how many patients the hospitals should prepare for.
Explain your reasoning.
Approximately 253 new cases.
253 1.82   4605
4605 .08  368
Hospitals should prepare for a maximum number of new patients per day to be about 368 .
3. The population of a city for various years since 1970 is show in the table.
a) What is a model for the data using regression?
Let 1970 be year 0 = x.
Linear R 2  .9541
Quadratic
R 2  .9831
Exponential R 2  .9838
Exponential Regression y  1.503 1.030
x
b) Because of mountains around the city, the size of the city is limited to about 375 square miles. City
planners need to decide to build a new mass transit system. From a study on ticket pricing, planners
know that a population density of 17,000 people per square mile the system will lose $.25 per rider. The
study also shows that a density of 19,000 people per square mile, the system will earn $.25 per rider.
Make a judgment based on the model to decide when the city should build the new mass transit sytem.
Recommend a population density so that the system doesn’t lose money.
Use the average 18,000 people per square mile as the break even point.
18,000  375  6,750,000 or 6.75 million people
The population will be 6.75 million, with a density of 18,000 people
per square mile when x  50.354 which will be in 2020.