Answer:
C) y = (1/4)^(-x)
Explanation:
The average rate of change on an interval [a, b] is found using the formula ...
arc = (f(b) -f(a))/(b -a)
For an exponential function with base b on interval [2, 3], the rate of change is ...
arc = (b^3 -b^2)/(3 -2) = b^2(b -1)
This expression assumes a positive sign on the exponent.
We can compute the arc for each answer choice as ...
(reference) 1/3^-x = 3^x ⇒ arc = 3²(3 -1) = 18
A) 2^x ⇒ arc = 2²(2 -1) = 4
B) 5^(x-2) = (1/25)5^x ⇒ arc = (1/25)(5²)(5 -1) = 4
C) 1/4^-x = 4^x ⇒ arc = 4²(4 -1) = 48
D) (2/3)^-x = (3/2)^x ⇒ arc = (3/2)²(3/2 -1) = 9/8
An average rate of change greater than 18 is demonstrated by (1/4)^-x.