Rewrite the function f(x)= 0.25(0.5) -3^x in the form f(x) = a(b)^x
Then: when x increases by 1, the function increases or decreases by a factor of 0.5, 0.25, 1/8, 8.
f(x) = 0.25(0.5)^x - 3^x
When x increases by 1:
f(x+1) = 0.25(0.5)^{x+1} - 3^{x+1}
= 0.25(0.5)^x(0.5) - 3*3^x
= 0.25(0.5)^x(0.5) - 3*3^x
= 0.25(0.5)^x * 0.5 - 3(3^x)
Thus, when x increases by 1, the function decreases by a factor of 1/8.