13 – Exponential vs. Linear Functions Calculator Required Exponential Investigations – Functions 13 – Exponential vs. Linear Functions Calculator Required

Linear and Exponential Relationships - Tables 2 4 6 2 1 2 x –2 4 10 f(x) 5 8 14 23 x 5 7 8 10 f(x) 11 1 +3 +6 +9 –4 –2 –4 Increasing Linear Decreasing Linear The common difference is 3/2. The common difference is –2.

Linear and Exponential Relationships - Tables 2 2 1 2 2 1 x 2 4 5 f(x) 1 16 32 x 2 4 5 f(x) 1 16 32 +3 +12 +16 x 4 x 4 x 2 For every increase of 1, multiply by 2. Not Linear Exponential Growth The common ratio is 2/1 = 2

Linear and Exponential Relationships - Tables 3 6 3 3 6 3 x –1 2 8 11 f(x) 12 4 4/9 4/27 x –1 2 8 11 f(x) 12 4 4/9 4/27 –8 –10/3 –8/27 x 1/3 x 1/9 x 1/3 For every increase of 3, multiply by 1/3. Not Linear Exponential Decay The common ratio is 1/9.

1. Linear and Exponential Relationships - Tables Based on the values given in the table, identify the function as: Exponential growth Exponential decay Linear increasing Linear decreasing Find the common ratio (r) or common difference (d). 2 2 2 Exponential Growth x –1 1 3 5 f(x) 1/2 2 8 32 r = 4/2 = 2 x 4 x 4 x 4

2. Linear and Exponential Relationships - Tables Based on the values given in the table, identify the function as: Exponential growth Exponential decay Linear increasing Linear decreasing Find the common ratio (r) or common difference (d). 4 2 3 Linear Increasing x –5 –1 1 4 f(x) –8 20 34 55 d = 7 +28 +14 +21

3. Linear and Exponential Relationships - Tables Based on the values given in the table, identify the function as: Exponential growth Exponential decay Linear increasing Linear decreasing Find the common ratio (r) or common difference (d). 3 3 3 Linear Decreasing x 3 6 9 f(x) 16 12 8 4 d = –4/3 –4 –4 –4

4. Linear and Exponential Relationships - Tables Based on the values given in the table, identify the function as: Exponential growth Exponential decay Linear increasing Linear decreasing Find the common ratio (r) or common difference (d). 2 1 1 Exponential Decay x 6 8 9 10 f(x) 64 16 4 r = 1/2 x 1/4 x 1/2 x 1/2

5. Linear and Exponential Relationships - Tables Based on the values given in the table, identify the function as: Exponential growth Exponential decay Linear increasing Linear decreasing Find the common ratio (r) or common difference (d). 2 2 2 Exponential Growth x –5 –3 –1 1 f(x) 32/9 8 18 81/2 r = 9/8 x 9/4 x 9/4 x 9/4

6. Linear and Exponential Relationships - Tables Based on the values given in the table, identify the function as: Exponential growth Exponential decay Linear increasing Linear decreasing Find the common ratio (r) or common difference (d). 2 6 4 Linear Decreasing x –10 –8 –2 2 f(x) 4 1 –14 d = –3/2 –3 –9 –6

7. Linear vs. Exponential Models – Creating an Equation Initial Value: 1000 Change (in words): appreciates at 5% If linear, common difference: d = If exponential, rate (as decimal): 0.05 If exponential, growth/decay factor: common ratio r = 1.05

8. Linear vs. Exponential Models – Creating an Equation Initial Value: 200 Change (in words): decreases by 15 If linear, common difference: d = –15 If exponential, rate (as decimal): If exponential, growth/decay factor: common ratio r =

9. Linear vs. Exponential Models – Creating an Equation Initial Value: 600 Change (in words): doubles If linear, common difference: d = If exponential, rate (as decimal): 1.00 If exponential, growth/decay factor: common ratio r = 2.00

10. Linear vs. Exponential Models – Creating an Equation Initial Value: 800 Change (in words): decreases by 20% If linear, common difference: d = If exponential, rate (as decimal): 0.20 If exponential, growth/decay factor: common ratio r = 0.80

From your PowerPoint notes, complete 12-20 in groups. 11. Linear vs. Exponential Models – Creating an Equation Initial Value: 500 Change (in words): increases by 100 If linear, common difference: d = 100 If exponential, rate (as decimal): If exponential, growth/decay factor: common ratio r = From your PowerPoint notes, complete 12-20 in groups.

12-20. Linear vs. Exponential Models – Creating an Equation

21. Linear vs. Exponential Models – Creating an Equation A function has an initial value of 200 hours and decreases by 10 hours (t) every hour. Write a function f(t) which represents the scenario. A function has an initial value of 200 hours and decreases by 10 hours (t) every hour. Write a function f(t) which represents the scenario. decreases by 10 hours (t) every hour – linear…..d = –10 f(t) = 200 – 10t

22. Linear vs. Exponential Models – Creating an Equation A function has an initial value of $1000 and increases 7% each year (t). Write a function f(t) which represents the scenario. A function has an initial value of $1000 and increases 7% each year (t). Write a function f(t) which represents the scenario. Increases 7% each year – exponential….r = 1.07

23. Linear vs. Exponential Models – Creating an Equation A function has an initial value of $250 and increases $25 each year (t). Write a function f(t) which represents the scenario. A function has an initial value of $250 and increases $25 each year (t). Write a function f(t) which represents the scenario. Increases $25 each year – linear…d = 25

24. Linear vs. Exponential Models – Creating an Equation A function has an initial value of $900 and decreases 5% each month (t). Write a function f(t) which represents the scenario. A function has an initial value of $900 and decreases 5% each month (t). Write a function f(t) which represents the scenario. Decreases 5% each month – exponential….r = 0.95

25. Linear vs. Exponential Models – Creating an Equation A function has an initial value of $1000 and appreciates 12% each year (t). Write a function f(t) which represents the scenario. A function has an initial value of $1000 and appreciates 12% each year (t). Write a function f(t) which represents the scenario. Appreciates 12% each year – exponential….r = 1.12