To determine the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( y = 2 \left(4^z\right) \)[/tex], we need to understand the concept of a [tex]\( y \)[/tex]-intercept. The [tex]\( y \)[/tex]-intercept of a graph is the point where the graph crosses the [tex]\( y \)[/tex]-axis. At this point, the value of [tex]\( z \)[/tex] is 0.
Given the equation [tex]\( y = 2 \left(4^z\right) \)[/tex], we substitute [tex]\( z = 0 \)[/tex] into the equation to find the corresponding [tex]\( y \)[/tex]-value.
1. Start with the equation:
[tex]\[
y = 2 \left(4^z\right)
\][/tex]
2. Substitute [tex]\( z = 0 \)[/tex]:
[tex]\[
y = 2 \left(4^0\right)
\][/tex]
3. Evaluate [tex]\( 4^0 \)[/tex]:
[tex]\[
4^0 = 1
\][/tex]
4. Now, multiply by 2:
[tex]\[
y = 2 \times 1 = 2
\][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( y = 2 \left(4^z\right) \)[/tex] is [tex]\( (0, 2) \)[/tex].
The correct answer is:
B. [tex]\((0, 2)\)[/tex]
