Question

Let f(x)=−log(4x)+5.

Answer 1

To solve the average rate of change, use the formula of the slope:
m = ( y2 - y1 ) / ( x2 - x1 )
but first we must solve the value of the function when x = 3

f(3) = - log ( 4 * 3 ) + 5
f (3) = 3.92

solve the function when x = 8
f(8) = - log ( 4 * 8) + 5
f(8) = 3.49

so the average rate of change
m = ( 3.49 - 3.92 ) / ( 8 - 3)
m = - 0.09

Answer 2

Answer:

Average rate of change = .09

Step-by-step explanation:

Rate of change of the given function can be represented by the formula

$m = \frac{y-y'}{x-x'}$

For f(x) = y = -log(4x) + 5

For x = 3

y = -log(12) + 5

y = -1.08 + 5 = 3.92

For x = 8

y' = -log(32) + 5

y' = -1.51 + 5 = 3.49

Now applying these values in the given formul$m=\frac{(3.92-3.49)}{(8 - 3)}=-\frac{0.425}{(5)}=(0.085)=(0.09)$