To determine the growth rate of the exponential function [tex]\( y = 3 \cdot 2^x \)[/tex], we need to interpret the structure of this equation.
An exponential function is typically of the form [tex]\( y = a \cdot b^x \)[/tex], where:
- [tex]\( a \)[/tex] is the initial value (or the coefficient),
- [tex]\( b \)[/tex] is the base of the exponential function, and
- [tex]\( x \)[/tex] is the exponent or the variable.
In our function [tex]\( y = 3 \cdot 2^x \)[/tex]:
- [tex]\( a \)[/tex] is 3, which represents the initial value.
- [tex]\( b \)[/tex] is 2, which is the base and also signifies the factor by which the function grows for each increment in [tex]\( x \)[/tex].
The growth rate of an exponential function is determined by the base [tex]\( b \)[/tex] of the exponential expression [tex]\( b^x \)[/tex]. Hence, the growth rate is the value of [tex]\( b \)[/tex].
In our case, the base [tex]\( b \)[/tex] is 2.
Therefore, the growth rate of the function [tex]\( y = 3 \cdot 2^x \)[/tex] is:
b. 2
So, the best answer provided is:
B
