Answer:
[tex]y=10(2)^{x}[/tex]
Step-by-step explanation:
Given:
The graph of [tex]y=-3x+2[/tex] intersects the exponential function at [tex](-1,5)[/tex].
So, the point [tex](-1,5)[/tex] must also lie on the exponential function.
Let us check each option for [tex]y[/tex] value at [tex]x = -1[/tex].
The option that gives [tex]y= 5[/tex] is the correct option.
Option 1:
[tex]y=10(2)^{x}\\y=10(2)^{-1}\\y=10\times \frac{1}{2}=\frac{10}{2}=5[/tex]
Option 2:
[tex]y=10(0.5)^{x}\\y=10(0.5)^{-1}\\y=10\times \frac{1}{0.5}=\frac{10}{0.5}=20[/tex]
Option 3:
[tex]y=5^{x}\\y=5^{-1}\\y=\frac{1}{5}=0.2[/tex]
Option 4:
[tex]y=5(2)^{x}\\y=5(2)^{-1}\\y=5\times \frac{1}{2}=\frac{5}{2}=2.5[/tex]
Therefore, only option 1 gives 5 for [tex]y[/tex] when [tex]x=-1[/tex]
So, the correct option is [tex]y=10(2)^{x}[/tex]
