1

Problem

For x > 0, which of the following is true about the values of \$4^x\$ and 3x + 2?

2

Step

Understand the properties of exponential functions:

→ \$4^x\$ is an exponential function where the base is 4 and the exponent is x.
→ Exponential functions with a base greater than 1 increase exponentially as x increases and decrease exponentially as x decreases.

3

Step

Determine the stem function:

→ The stem function, denoted as \$4^x\$, means to find the stem value of \$4^x\$.
→ The stem function rounds the value of \$4^x\$ to the nearest integer.

4

Step

Compare with linear function:

→ The function 3x+2 represents linear growth.
→ As x increases, the value of 3x+2 increases at a constant rate.

5

Step

Choosing the correct option:

As x increases, the values of \$4^x\$ increase exponentially.

6

Sumup

Please summarize steps

Choices

7

Choice-A

This option suggests that as x increases, the values of \$4^x\$ decrease exponentially. This contradicts the properties of exponential functions because as x increases, \$4^x\$ increases

Wrong As x increases, the values of \$4^x\$ decrease exponentially.

8

Choice-B

This option suggests that as x increases, the values of \$4^x\$ increase exponentially. This aligns with the properties of exponential functions because as x increases, \$4^x\$ increases

Correct As x increases, the values of \$4^x\$ increase exponentially.

9

Choice-C

This choice contradicts the properties of exponential functions because as x decreases, \$4^x\$ decreases

Wrong As x decreases, the values of \$4^x\$ increase exponentially.

10

Choice-D

This choice implies that \$4^x\$ decreases exponentially as x decreases, which is also incorrect for positive values of x

Wrong As x decreases, the values of \$4^x\$ decrease exponentially.

11

Answer

Option

B

12

Sumup

Please summarize choices