The curve through the ordered pairs (0, 10), (1, 5), and (2, 2.5) can be represented by the function f(x) = 10(0.5)x. What is the multiplicative rate of change of the function?

I think your equation should be f(x) = 10(.5)^x

notice:
10(.5) = 5
5(.5) = 2.5
2.5(.5) = 1.25 <---- not shown, but I multiplied each f(x) value by .5 to
get the next one, so what do you think?