To identify the dependent variable of the function described, let's first understand the structure of the given equation:
[tex]\[ g(V) = 40V + 15 \][/tex]
This equation describes the relationship between the number of gum balls [tex]\( g \)[/tex] and the volume [tex]\( V \)[/tex] of the box in cubic units.
### Step-by-Step Analysis:
1. Understanding the variables:
- [tex]\( g(V) \)[/tex]: This denotes the number of gum balls that can be packaged in a box. The notation [tex]\( g(V) \)[/tex] implies that [tex]\( g \)[/tex] is a function of [tex]\( V \)[/tex], meaning [tex]\( g \)[/tex] depends on [tex]\( V \)[/tex].
- [tex]\( V \)[/tex]: This represents the volume of the box in cubic units.
2. Identifying the independent variable:
- The independent variable is the variable that we can change freely. In this case, the independent variable is [tex]\( V \)[/tex], as it represents the volume of the box that can vary.
3. Identifying the dependent variable:
- The dependent variable is the variable that depends on the value of another variable. Here, the number of gum balls [tex]\( g \)[/tex] changes depending on the volume [tex]\( V \)[/tex]. Therefore, [tex]\( g \)[/tex] is dependent on [tex]\( V \)[/tex].
Since [tex]\( g \)[/tex] changes with [tex]\( V \)[/tex] and is given as a function of [tex]\( V \)[/tex], we can conclusively say that the dependent variable in this function is:
[tex]\[ \boxed{g} \][/tex]
