What is the equation of the exponential graph shown? : '(

Exponential functions fit the template
y = a*b^x
where 'a' and b are fixed values

The value of 'a' is the y intercept. In this case, it is 100 since (0,100) is on the curve. This is the part where the graph crosses the y axis. So a = 100.

The value of b takes a bit of work to find. We'll plug a = 100, x = 1 and y = 50 into the equation shown above. Why x = 1 and y = 50 you might ask? Well the point (1,50) appears to be on the graph as well.

So plugging those three items into the equation leads to
y = a*b^x
50 = 100*b^1
50 = 100*b
50/100 = 100*b/100 ... divide both sides by 100
1/2 = b
b = 1/2 
b = 0.5

So the equation is y = 100*(1/2)^x which can be written as y = 100*(0.5)^x

The value of b = 1/2 = 0.5 indicates that we multiply each previous result by 1/2 = 0.5 to get the next result. This is another way of saying "divide each result by 2 to get the next"

Eg: 
100 ---> 50 ---> 25 etc