AnswersHigh School Math 2 AComparing Exponential, Linear, and Quadratic Growth

Comparing Exponential, Linear, and Quadratic Growth Answers

16 verified answers
1
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According to the table, which function grows the fastest? The linear functionThe quadratic function✔ The exponential function

A
The linear function
B
The quadratic function
C
✔ The exponential function
2
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By what factor does the y-value change for y = 4x? 23✔ 45

A
2
B
3
C
✔ 4
D
5
3

Compared to an exponential function y = b, where b > 0, a quadratic function grows:

Question illustration
A
slower
B
faster
C
at the same rate
D
sometimes faster, sometimes slower
4

Complete the table for each function. Then answer the questions that follow.a= ⇒ 4 ; b = ⇒ 4; c = ⇒ 8; d = ⇒ 16; e = ⇒ 12; f = ⇒ 36; g = ⇒ 64

Answer:

64

5

After what y-value does the exponential function appear to surpass the linear function?

Answer:

4

6

After approximately what y-value does the exponential function surpass the quadratic function?

Answer:

80

7

Which function grows the fastest? the linear functionthe quadratic function✔ the exponential function

A
the linear function
B
the quadratic function
C
✔ the exponential function
8

Consider the function y = 8x. How do the y-values of this function grow?

A
by adding 8
B
by multiplying the previous y-value by 8
C
by adding 8, then 16, then 32…
9

Consider the function y = 3x2. How do the y-values of this function grow?

A
by adding 3
B
by adding 9
C
by multiplying the previous y-value by 3
D
by adding 3, then 9, then 15, …
10

If Anita and Miguel do not take any money from their accounts, whose account will grow faster? Explain why.

Answer:

Miguel's account will grow faster. Anita's account shows linear growth because it increases by a constant amount each month. Miguel's account shows exponential growth because it increases by a percentage of the total. In the long run, exponential growth will always surpass linear growth.

11

Which of the following did you include in your answer?

A
Anita’s account had linear growth.
B
Miguel’s account had exponential growth.
C
Miguel’s account grew faster because exponential growth is faster than linear growth.
12

On equal intervals, the y-values of a quadratic function have a common difference ✔ second difference ratio

A
difference
B
✔ second difference
C
ratio
13

Compare the functions y = 2x2 and y = 2x. Which of the following statements are true? Check all that apply.

A
For any x-value, the y-value of the exponential function is always greater.
B
For any x-value, the y-value of the exponential function is always smaller.
C
For some x-values, the y-value of the exponential function is smaller.
D
For some x-values, the y-value of the exponential function is greater.
E
For any x-value greater than 7, the y-value of the exponential function is greater.
F
For equal intervals, the y-values of both functions have a common ratio.
14

Which function grows the slowest?✔ the linear functionthe quadratic functionthe exponential function

A
✔ the linear function
B
the quadratic function
C
the exponential function
15

Consider the function y = 15x. How do the y-values of this function grow?

A
by adding 15
B
by multiplying the previous y-value by 15
C
by adding 15, then 30, then 45…
16

Compared to a linear function, a quadratic function grows slower ✔ faster at the same rate sometimes faster sometimes slower

A
slower
B
✔ faster
C
at the same rate
D
sometimes faster sometimes slower

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