Question

Write an exponential equation for the graph. I’m clearly doing something wrong and I’m not sure what it is.

Answer 1

Given

Graph

Find

Exponential equation for the graoh

Explanation

Exponential equation is in the form of

$y=ab^x$

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)

$\begin{gathered} -3=a(b)^0 \\ a=-3 \end{gathered}$

and

$\begin{gathered} -6=-3b^{-1} \\ 2=b^{-1} \\ b=\frac{1}{2} \end{gathered}$

so , equation is

$y=-3(\frac{1}{2})^x$

Final Answer

Therefore , the exponential equation for the graph is

$y=-3(\frac{1}{2})^x$