Answered

Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Ask your questions and receive precise answers from experienced professionals across different disciplines. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Identify the type of function represented by [tex]\( f(x) = 4 \cdot 2^x \)[/tex].

A. Increasing linear
B. Decreasing linear
C. Exponential decay
D. Exponential growth

Sagot :

GinnyAnswer
To identify the type of function represented by [tex]\( f(x) = 4 \cdot 2^x \)[/tex], let's analyze the function step-by-step.

1. Form of the Function:
- The given function is [tex]\( f(x) = 4 \cdot 2^x \)[/tex].
- This is in the form of [tex]\( f(x) = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] and [tex]\( b \)[/tex] are constants and [tex]\( x \)[/tex] is the variable.

2. Identifying Exponential Functions:
- Functions of the form [tex]\( f(x) = a \cdot b^x \)[/tex] are classified as exponential functions.
- If [tex]\( b > 1 \)[/tex], the function represents exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
- In our function, [tex]\( a = 4 \)[/tex] and [tex]\( b = 2 \)[/tex].

3. Analyzing the Base (b):
- Here, [tex]\( b = 2 \)[/tex].
- Since [tex]\( 2 > 1 \)[/tex], the function [tex]\( f(x) = 4 \cdot 2^x \)[/tex] represents exponential growth.

4. Conclusion:
- Based on the condition that [tex]\( b > 1 \)[/tex], the function [tex]\( f(x) = 4 \cdot 2^x \)[/tex] must be classified as an exponential growth function.

Therefore, the correct answer is:

D. Exponential growth
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.