Use the table to answer the question.

Question

Term Number 1 2 3 4 5 6
Sequence for Function A 2.1 4.47 9.261 19.448 40.841 85.766
Sequence for Function B 2.7 5.4 8.1 10.8 13.5 16.2
Consider the sequences for Function A and Function B. Compare the growth rates of the functions. Which function is linear, and which function is exponential?

(1 point)
Responses

Initially, Function B has the greater growth rate. However, the growth rate of Function A quickly surpasses the growth rate of Function B. Function A is linear and Function B is exponential.
Initially, Function B has the greater growth rate. However, the growth rate of Function A quickly surpasses the growth rate of Function B. Function A is linear and Function B is exponential.

Initially, Function B has the greater growth rate. However, the growth rate of Function A quickly surpasses the growth rate of Function B. Function A is exponential and Function B is linear.
Initially, Function B has the greater growth rate. However, the growth rate of Function A quickly surpasses the growth rate of Function B. Function A is exponential and Function B is linear.

Function A always has the greater growth rate. Function A is exponential and Function B is linear.
Function A always has the greater growth rate. Function A is exponential and Function B is linear.

Function A always has the greater growth rate. Function A is exponential and Function B is linear.

Answer 1

To analyze the growth rates of the sequences for Function A and Function B, let's break down the information provided.

Sequence for Function A:

• 1: 2.1
• 2: 4.47
• 3: 9.261
• 4: 19.448
• 5: 40.841
• 6: 85.766

Sequence for Function B:

• 1: 2.7
• 2: 5.4
• 3: 8.1
• 4: 10.8
• 5: 13.5
• 6: 16.2

From the data:

1. Function A does not increase at a constant rate; the differences between the terms are increasing. This indicates a rapid growth pattern typically associated with exponential functions.

   • Differences:
     • 4.47 - 2.1 = 2.37
     • 9.261 - 4.47 = 4.791
     • 19.448 - 9.261 = 10.187
     • 40.841 - 19.448 = 21.393
     • 85.766 - 40.841 = 44.925

2. Function B consistently increases by the same amount (2.7 each time). This indicates a linear function.

   • Differences:
     • 5.4 - 2.7 = 2.7
     • 8.1 - 5.4 = 2.7
     • 10.8 - 8.1 = 2.7
     • 13.5 - 10.8 = 2.7
     • 16.2 - 13.5 = 2.7

Given these observations:

• Function A is exponential because its growth rate accelerates and does not remain constant.
• Function B is linear because it increases by the same amount with each term.

As for the growth rates:

• Initially, Function B has higher values than Function A for smaller term numbers. However, as we observe term 3 and beyond, the values of Function A's terms grow much faster and surpass those of Function B.

Thus, based on the analysis, the best response is:

Function A always has the greater growth rate. Function A is exponential and Function B is linear.