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"
Answer: f(x) = 100/(2ˣ) cause your points are (0, 100), (1, 50), (2, 25), and (3, 12.5) so it's decaying by half everytime the x-value gets bigger. The graph starts at 100 and decays by 1/2 everytime making the equation f(x) = 100/(2ˣ).
