Math 1
Lesson 6: Getting Down to Business
Learning Target(s): I can compare the similarities and differences in the growth of linear and
exponential models.
Directions: Create a graph and a table for each of the functions below. Then, answer the questions.
Function A:
Table:
Graph:
1
𝑦𝑦 = 2𝑥𝑥 + 5
x
0
1
2
3
4
5
y
Function B: 𝑦𝑦 = ∙ 2𝑥𝑥
Table:
Graph:
1. Which function is linear?
2. Which function is exponential?
3. Which function has a greater output when x is 0?
4. Which function has a greater output when x is 5?
5. Compare the growth rates of the two functions.
2
x
0
1
2
3
4
5
y
Function C:
Table:
Graph:
𝑦𝑦 = 3 ∙ 5𝑥𝑥
x
0
1
2
3
4
Function D: 𝑦𝑦 = 5𝑥𝑥 + 3
y
Table:
Graph:
6. Which function is linear?
7. Which function is exponential?
8. Compare the outputs of both functions when x is 0.
9. Which function has a greater output when x is 2?
10. Compare the growth rates of the two functions.
x
0
1
2
3
4
y
Math 1
Lesson 6: Getting Down to Business
Directions: Create a graph and a table for each of the functions below. Then, answer the questions.
Function A:
Table:
Graph:
1
𝑦𝑦 = 2𝑥𝑥 + 5
x
0
1
2
3
4
5
y
5
7
9
11
13
15
Function B: 𝑦𝑦 = ∙ 2𝑥𝑥
Table:
Graph:
2
x
0
1
2
3
4
5
y
0.5
1
2
4
8
16
1. Which function is linear?
Function A is linear
2. Which function is exponential?
Function B is exponential
3. Which function has a greater output when x is 0?
Function A has a greater output when x is 0.
4. Which function has a greater output when x is 5?
Function B has a greater output when x is 5.
5. Compare the growth rates of the two functions.
Function A grows slower because it is linear with a slope of 2. Function B grows faster
because it is exponential with a constant ratio of 2.
Function C:
Table:
Graph:
𝑦𝑦 = 3 ∙ 5𝑥𝑥
x
0
1
2
3
4
Function D: 𝑦𝑦 = 5𝑥𝑥 + 3
y
3
15
75
375
1875
Table:
Graph:
x
0
1
2
3
4
y
3
8
13
18
23
6. Which function is linear?
Function D is linear.
7. Which function is exponential?
Function C is exponential.
8. Compare the outputs of both functions when x is 0.
Both functions have an output of 3 when x is 0. They both have a y-intercept of (0, 3).
9. Which function has a greater output when x is 2?
Function C has a greater output when x is 2.
10. Compare the growth rates of the two functions.
Function C grows faster because it is exponential with a constant ratio of 5. Function D
grows slower because it is linear with a slope of 5.