1. 13 – Exponential vs. Linear Functions Calculator Required
Exponential Investigations – Functions
13 – Exponential vs. Linear Functions Calculator Required

2. Linear and Exponential Relationships - Tables2 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.

3. Linear and Exponential Relationships - Tables2 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

4. Linear and Exponential Relationships - Tables3 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.

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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 =

13. 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

14. 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

15. 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 in groups.

16. 12-20. Linear vs. Exponential Models – Creating an Equation

17. 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

18. 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

19. 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

20. 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

21. 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