Download Exponential Regression Homework: Modeling Data Patterns Name

Exponential Regression Homework: Modeling Data Patterns
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1. A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over
an 8-minute period.
Time in Minutes (x)
Temperature in Degrees Fahrenheit (y)
0
180
2
165
4
146
6
135
10
110
8
127
a. Use your calculator to find both linear and exponential regression models for the given data pattern. Also, record the “r” value.
linear model (round to 2 decimal places):___________________
Correlation Coefficient “r” (round to 4 decimal places):
exponential model (round to 2 decimal places):________________ Correlation Coefficient “r” (round to 4 decimal places):
b. Which model fits better? How did you decide?
2. The table below shows the number of new stores in a coffee shop franchise that opened during the years 2010 to 2015.
Year
Number of New Stores
2010
2011
2012
2013
2014
2015
48
80
153
261
403
681
a. Use your calculator to find both linear and exponential regression models for the given data pattern. Also, record the “r” value for each
rounded to FOUR decimal places. USE X=0 FOR 2010, ETC.
linear model (round to 2 decimal places):___________________
Correlation Coefficient “r” (round to 4 decimal places):
exponential model (round to 2 decimal places):________________ Correlation Coefficient “r” (round to 4 decimal places):
b. Which model fits better? How did you decide?
3. In order to safely build suspension bridges, the strength of steel cables must be tested. The breaking strength y, in tons, of steel cable
with diameter d, in inches, is given in the table below.
Diameter of Cable (inches)
Breaking Strength in Tons (y)
0.50
9.85
0.75
21.80
1.00
38.30
1.25
59.20
1.75
114.00
1.50
84.40
a. Write the exponential regression equation, rounding your “a” and “b” values to the nearest tenth (one decimal place).
4. A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that land heads up are counted and
returned to the box. The process is repeated and the data is recorded below.
Trial
Coins Heads Up
0
1,000
1
610
3
220
4
132
6
45
a. Write the exponential regression equation, rounding your “a” and “b” values to the nearest tenth (one decimal place).
5. The data collected by a biologist showing the growth of a colony of bacteria at the end of each hour are displayed in the table below.
Time (hours)
Population
0
250
1
330
2
580
3
800
4
1650
5
3000
a.
Write an exponential regression equation to model the data. (Round to two
decimal places).
b.
Using this equation, predict the population of bacteria (to the nearest whole
number) at the end of 7 hours.
6. The accompanying table shows the average salary of baseball players since 2000.
Number of Years
Since 2000
Average Salary
(thousands of dollars)
0
290
1
320
2
400
3
495
4
600
5
700
6
820
7
1000
8
1250
9
1580
a.
Write an exponential regression equation to model the data
(Round to two decimal places).
b.
Using this equation, predict the average salary THIS year!