Question

Write the function associated with the graph below

Answer 1

Since the value of the function is decreasing exponentially as x decreases ,

The function is of the form $y=ae^{bx}+c,b>0$.

Since the curve passes through (0,6),

$6=ae^{0}+c,6=a+c$,

Since the curve passes through (-1,0),

$0=ae^{-b}+c$.

Since $y=-3$ is a horizontal asymptote,

$-3=ae^{-\infty}+c,c=-3$

From the above 3 equations,

$c=-3,a=9,9e^{-b}=3,e^b=3,b=\ln 3$.

Therefore, the required function is

$y=9e^{\ln 3 x}-3\\ y=9*3^{ x}-3$.

It can be verified that the curve $y=9*3^{ x}-3$ passes through $(-2,-2)$.

Answer 2

That's a positive slope... I don't know if that's the kind of answer you're looking for, but it's a start I guess.