The function [tex]\( f(x) = 4 \cdot 2^x \)[/tex] is given. To determine the type of function, let’s analyze its components.
1. Identify the form of the function: This function [tex]\( f(x) = 4 \cdot 2^x \)[/tex] consists of a constant (4) multiplied by an exponential component [tex]\( 2^x \)[/tex].
2. Characteristics of exponential functions: Exponential functions can generally be written in the form [tex]\( f(x) = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] is a constant and [tex]\( b \)[/tex] is the base of the exponential function.
3. Determine the base [tex]\( b \)[/tex]: In this function, the base [tex]\( b \)[/tex] is 2.
4. Compare the base [tex]\( b \)[/tex] with 1:
- If [tex]\( b > 1 \)[/tex], the function exhibits exponential growth.
- If [tex]\( 0 < b < 1 \)[/tex], the function represents exponential decay.
Given that the base [tex]\( b = 2 \)[/tex] is greater than 1, the function [tex]\( 4 \cdot 2^x \)[/tex] represents exponential growth.
Thus, the correct answer is:
B. Exponential growth
