Respuesta :
The exponential equation is [tex]f(x)=-3(2)^x[/tex]
Explanation:
The points are [tex]$(1,-6)$[/tex] and [tex]$(2,-12)$[/tex]
To determine the exponential equation, let us substitute the points in the exponential equation [tex]y=a(b)^x[/tex]
Substituting [tex]$(1,-6)$[/tex] in the equation [tex]y=a(b)^x[/tex], we get,
[tex]-6=a(b)^1[/tex]
[tex]-6=ab[/tex]
[tex]\frac{-6}{b} =a[/tex]
Thus, substituting [tex]\frac{-6}{b} =a[/tex] and [tex]$(2,-12)$[/tex] in [tex]y=a(b)^x[/tex], we have,
[tex]-12=\frac{-6}{b} (b)^2[/tex]
[tex]-12=-6b[/tex]
[tex]2=b[/tex]
Substituting [tex]b=2[/tex] in [tex]\frac{-6}{b} =a[/tex], we get,
[tex]\frac{-6}{2} =a\\[/tex]
[tex]-3=a[/tex]
Hence, substituting the value of a and b in the exponential equation [tex]y=a(b)^x[/tex], we have,
[tex]y=-3(2)^x[/tex]
Thus, the exponential equation is [tex]f(x)=-3(2)^x[/tex]
