Comparing Exponential, Linear, and Quadratic Growth

Question 1

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

Revolt · Accepted Answer

64

Question 2

By what factor does the y-value change for y = 4x? 23✔ 45

Revolt · Accepted Answer

✔ 4

Question 3

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

Revolt · Accepted Answer

✔ the exponential function

Question 4

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

Revolt · Accepted Answer

✔ The exponential function

Question 5

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

Revolt · Accepted Answer

80

Question 6

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

Revolt · Accepted Answer

4

Question 7

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

Revolt · Accepted Answer

by adding 8

Question 8

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

Revolt · Accepted Answer

by adding 3, then 9, then 15, …

Question 9

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

Revolt · Accepted 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.

Question 10

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

Revolt · Accepted Answer

slower

Comparing Exponential, Linear, and Quadratic Growth Answers

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