1. Warm up honors algebra 2 3/7/19
Pick up the handout by the projector and begin working on it  “Exponential Practice”
Applying same base exponentials

2. Reminder on Regressions
1. Perform a linear regression on the following data:
2. Perform a quadratic regression on the following data: x 1 2 3 4 5 6
f(x)
3.45
8.7
13.95
19.2
24.45
29.7 x 1 2 6 11 13
f(x) 3 39
120
170

3. Calculator reminder!!
How to find the curve of best fit when given a data table:
Enter data into table on calculator
 STAT  EDIT (1)  x-values in L1  y- values in L2
Determine the type of function the data represents
- Linear, Quadratic or Exponential

4. Calculator reminder (cont):
STAT  tab over to CALC  select type of function  Enter through
4: LinReg(ax+b) (linear)
5: QuadReg (Quadratic)
0: ExpReg (Exponential)
9: LnReg (Natural Log)
Plug the given values into the function formula.

5. Curve of best fit = Regression
Examples:
“Find the curve of best fit for this linear data” = “Perform a linear regression”
“Perform a quadratic regression” = “Find the curve of best fit”

6. Linear functions (first degree)
First differences are constant!! x -1 1 2
f(x) 5 8 11
First differences are constant, so linear function!!
First Differences: +3 +3 +3

7. Quadratic functions (Second Degree)
Second differences are constant!! x -1 1 2
f(x) 3 5 8
First differences are NOT constant!! NOT Linear!!
First Differences: +1 +2 +3
Second differences are constant, so Quadratic!!
Second Differences: +1 +1

8. Exponential functions
First differences are NOT constant!! NOT Linear!!
Ratio of y-values are constant!! x -1 1 2
f(x) 16 24 36 54
Second differences are NOT constant!! NOT Quadratic!!
First Differences: +8
+12
+18
Second Differences: +4 +6
Ratios are constant, so Exponential!!
Ratios:
24 16 = = =1.5

9. Exponential with a constant ratio of 1.5.
Determine what type of function the data represents. Find the common difference or ratio. x -1 1 2 3
f(x)
2. 6 4 6 9
13.5
First Differences:
+1.3 4 +2 +3
+4.5
Second Differences:
+0.66 +1
+1.5
Exponential with a constant ratio of 1.5.
Ratios:
= 6 4 = 9 6 = =1.5

10. Linear with a first common difference of 5.
Determine what type of function the data represents. Find the common difference or ratio. x -1 1 2 3
f(x) −3 7 12 17
First Differences: +5 +5 +5 +5
Linear with a first common difference of 5.

11. Quadratic with a second common difference of 1
Determine what type of function the data represents. Find the common difference or ratio. x -1 1 2 3
f(x) 5 8 12
First Differences: +1 +2 +3 +4
Second Differences: +1 +1 +1
Quadratic with a second common difference of 1

12. Find an exponential model for the data
Find an exponential model for the data. Use the model to predict when the tuition at U.T. Austin will be $6000.
Enter data in the graphing calculator and use the exponential regression feature (0)
Year
Tuition
$3128
$3585
$3776
$3950
$4188
Mention that the r and r^2 show good fit
𝑓 𝑥 = 𝑥

13. Find an exponential model for the data
Find an exponential model for the data. Use the model to predict when the tuition at U.T. Austin will be $6000.
Graph the function
To enter the regression equation as Y1 from the screen, press , choose 5:Statistics, press , scroll to select the EQ menu, and select 1:RegEQ.

14. The tuition will be about $6000 when t = 9 or 2008–09.
Find an exponential model for the data. Use the model to predict when the tuition at U.T. Austin will be $6000.
7500 15
Enter 6000 as Y2. Use the intersection feature. You may need to adjust the dimensions to find the intersection.
The tuition will be about $6000 when t = 9 or 2008–09.

15. Use exponential regression to find a function that models this data
Use exponential regression to find a function that models this data. When will the number of bacteria reach 2000?
Time (min) 1 2 3 4 5 #
200
248
312
390
489
610
2500 15
The bacteria count at 2000 will happen at approximately 10.3 minutes.
𝑓 𝑥 = 𝑥

16. Find a natural log model for the data
Find a natural log model for the data. According to the model, when will the global population exceed 9,000,000,000?
Global Population Growth
Population (billions)
Year 1
1800 2
1927 3
1960 4
1974 5
1987 6
1999
𝑓 𝑥 = 𝑙𝑛𝑥
The population will exceed 9,000,000,000 (x=9) in the year 2058.

17. Use the logarithmic regression to find a function that models this data. When will the speed reach 8.0 m/s?
Time (min) 1 2 3 4 5 6 7
Speed (m/s)
0.5
2.5
3.5
4.3
4.9
5.3
5.6
Use the intersect feature to find y when x is 8. The time it will reach 8.0 m/s is 16.6 min.
𝑓 𝑥 = 𝑙𝑛𝑥