Answer: The answer is (D) [tex]f(x)=a^{(1-b)x}.[/tex]
Step-by-step explanation: We are given four exponential functions, out of which we are to select the one that represents exponential decay.
Given that the following function is an exponential growth function.
[tex]f(x)=a^{bx}.[/tex]
We take the values of a and b as 2 and 3 respectively so that the given function represents exponential growth.
We have drawn the graphs of all the four exponential functions taking these values of 'a' and 'b' in the attached figure.
We will see the the graph of the fourth function will show an exponential decay.
and the rest three will show exponential growth.
Thus, (D) is the correct option.
