Answer :
Exponential Equation
We are given the following values of x and y:
x={-2,-1,0,1,2,3}
y={12,6,3,3/2,3/4,3/8}
It's required to find the equation that models the table.
The model to use is exponential, which general formula is:
[tex]y=A\cdot r^x[/tex]Where A and r are values to determine with the data provided in the table.
Let's use the first two values: x=-2, y=12:
[tex]12=A\cdot r^{-2}[/tex]Now use the second pair: x=-1, y=6
[tex]6=A\cdot r^{-1}[/tex]Dividing the second equation by the first:
[tex]\begin{gathered} \frac{6}{12}=\frac{A\cdot r^{-1}}{A\cdot r^{-2}} \\ \text{Operating and simplifying:} \\ \frac{1}{2}=r^{(-1+2)}=r \end{gathered}[/tex]Thus, r = 1/2 = 0.5Thus
Substituting the value of r in any of the two equations (for example the first one):
[tex]12=A\cdot0.5^{-2}[/tex]Operating:
[tex]12=A\cdot4[/tex]Solving for A:Solving for A
A = 12/4 = 3
Thus, the required equation is:
[tex]y=3\cdot(0.5)^x[/tex]Note we only used two points to determine the equation. The rest of the points from the table should satisfty the equation. We'll only check one of them, for example x=0, y=3
[tex]y=3\cdot(0.5)^0=3\cdot1=3[/tex]The point satisfies the equation and the rest of the points will also dosfies the equation and
Answer: B
[tex]y=3\cdot(0.5)^x[/tex]