Write the function associated with the graph below

Question

asked Jun 23, 2019 202k views

2 Answers

Sbtourist · Answer 1 · 2019-06-27T17:38:22+0000

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

.

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