What is the growth rate of the function [tex][tex]$y=3 \cdot 2^x$[/tex][/tex]?

A. 3
B. 2
C. 1
D. 6

Please select the best answer from the choices provided:
A
B
C
D



Answer :

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