Given
Graph
Find
Exponential equation for the graoh
Explanation
Exponential equation is in the form of
[tex]y=ab^x[/tex]from graph, we see
when x = 0 then y = -3
and when x = -1 then y = -6
now substitute these points in equation ,
(0 , -3) and (-1 , -6)
[tex]\begin{gathered} -3=a(b)^0 \\ a=-3 \end{gathered}[/tex]and
[tex]\begin{gathered} -6=-3b^{-1} \\ 2=b^{-1} \\ b=\frac{1}{2} \end{gathered}[/tex]so , equation is
[tex]y=-3(\frac{1}{2})^x[/tex]Final Answer
Therefore , the exponential equation for the graph is
[tex]y=-3(\frac{1}{2})^x[/tex]