Question 189524
<font size = 8 color = "red"><b>Edwin's solution:

I claim it is a growth not a decay!</pre></font>
<pre><font size = 4 color = "indigo"><b>
It has to be growth because when x goes from a smaller value -2
to larger value 0, y also grows from a smaller value -20 to a 
larger value -5.  That is a growth.

We start with the basic exponential equation:

{{{y = A*B^x}}}

Then we substitute the point (0,-5)

{{{y = A*B^x}}}

{{{-5 = A*B^0}}}

{{{-5 = A*1}}}

{{{-5 = A }}}

So the exponential equation {{{y = A*B^x}}} is now

{{{y = -5*B^x}}}

Now we substitute the other point (-2, -20)

{{{-20 = -5*B^(-2)}}}

And simplify:

{{{-20 = -5*(1/B^2)}}}
 
Multiply both sides by {{{B^2}}}

{{{-20B^2 = -5}}}

Divide both sides by -20

{{{B^2 = (-5)/(-20)}}}

{{{B^2 = 1/4}}}

{{{B = sqrt(1/4)}}}

{{{B = 1/2}}}

So the equation {{{y = -5*B^x}}} is now

{{{y = -5*(1/2)^x}}}

The graph looks like this:

{{{graph(200,100,-3,3,-40,10,-5*(.5)^x)}}}

which shows it's a growth.

Edwin</pre>