what is the multiplicative rate of change for the exponential function $f(x)=2(\\frac{5}{2})^{-x}$?\n0.4\n0.6…
what is the multiplicative rate of change for the exponential function $f(x)=2(\\frac{5}{2})^{-x}$?\n0.4\n0.6\n1.5\n2.5
Answer
Explanation:
Step1: Rewrite the function
We know that (a^{-x}=\left(\frac{1}{a}\right)^{x}). So (f(x)=2\left(\frac{5}{2}\right)^{-x}=2\left(\frac{2}{5}\right)^{x}).
Step2: Identify the multiplicative - rate of change
For an exponential function of the form (y = ab^{x}), the multiplicative rate of change is (b). Here (b=\frac{2}{5}=0.4).
Answer:
0.4