what is the average rate of change for $f(x)=-3^{x}+79$ over the interval $2leq xleq4$?\na -124\nb -18\nc…

Explanation:

Step1: Find f(2)

Substitute x = 2 into f(x): $f(2)=-3^{2}+79=-9 + 79=70$

Step2: Find f(4)

Substitute x = 4 into f(x): $f(4)=-3^{4}+79=-81 + 79=-2$

Step3: Calculate average rate of change

The formula for average rate of change of a function f(x) over [a,b] is $\frac{f(b)-f(a)}{b - a}$. Here a = 2, b = 4. $\frac{f(4)-f(2)}{4 - 2}=\frac{-2-70}{2}=\frac{-72}{2}=-36$

Answer:

C. -36