Given the following exponential equation:
[tex]y=2\cdot(\frac{1}{2})^x[/tex]
For x = 0, we have:
[tex]y=2\cdot(\frac{1}{2})^0=2\cdot1=2[/tex]
Then, the y-intercept must be y = 2. Now, for x = -2:
[tex]y=2\cdot(\frac{1}{2}){}^{-2}=2\cdot(2)^2=2\cdot4=8[/tex]
Looking at D, we see that the y-intercept is 4, so this graph does not correspond to the equation. Looking at B and C, we see that y ≠ 8 for x = -2, so we discard them.
For A:
We see that y = 8 for x = -2, and the y-intercept is 2. Then, this is the corresponding graph of the equation.
Answer: A
