To find the [tex]\( y \)[/tex]-intercept of the graph of the equation [tex]\( y = 2 \left(4^x\right) \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0. The [tex]\( y \)[/tex]-intercept is where the graph intersects the [tex]\( y \)[/tex]-axis, which always occurs when [tex]\( x = 0 \)[/tex].
1. Start with the given equation:
[tex]\[ y = 2 \left(4^x\right) \][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
[tex]\[ y = 2 \left(4^0\right) \][/tex]
3. Simplify the expression inside the parentheses. Any number raised to the zero power is 1:
[tex]\[ 4^0 = 1 \][/tex]
4. Multiply the result by 2:
[tex]\[ y = 2 \times 1 \][/tex]
[tex]\[ y = 2 \][/tex]
So, when [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] equals 2. Therefore, the [tex]\( y \)[/tex]-intercept is:
[tex]\[ (0, 2) \][/tex]
Thus, the correct answer is:
A. [tex]\( (0, 2) \)[/tex]
