Question

What is the multiplicative rate of change for the exponential function f(x) = 2(5/2) -^x f start bracket x end bracket equals two start bracket five-halves end bracket superscript negative x?

0.4
0.6
1.5
2.5

Answer 1

Rewrite f(x) = 2(5/2)^{-x} = 2[(5/2)^{-1}]^{x} = 2(2/5)^{x}.
So the multiplicative rate of change (the factor f(x+1)/f(x)) is 2/5 = 0.4.