Respuesta :
EXPLANATION :
From the problem, we have the points :
[tex](1,-7),(2,-14),(3,14),(4,7)[/tex]The points represent an exponential function if all points satisfy the equation in the form :
[tex]y=ab^x[/tex]Let's try (1, -7)
[tex]\begin{gathered} -7=ab^1 \\ ab=-7 \end{gathered}[/tex](2, -14)
[tex]\begin{gathered} -14=ab^2 \\ -14=ab(b) \\ \text{ Note that ab = -7 from the first equation :} \\ -14=-7b \\ b=\frac{-14}{-7}=2 \end{gathered}[/tex]We have b = 2.
Using the first equation, solve for a :
[tex]\begin{gathered} ab=-7 \\ 2a=-7 \\ a=-\frac{7}{2} \end{gathered}[/tex]So the equation now will be :
[tex]\begin{gathered} y=ab^x \\ y=-\frac{7}{2}(2)^x \end{gathered}[/tex]Let's check the third and fourth points, they must satisfy the equation :
[tex]\begin{gathered} \text{ For \lparen3, 14\rparen} \\ 14=-\frac{7}{2}(2)^3 \\ 14=-\frac{7}{2}(8) \\ 14=-28 \\ 14=-28 \\ \text{ False!} \end{gathered}[/tex]Since the third point does NOT satisfy the equation, therefore, this is NOT an exponential function
