Question

PLEASE ANSWER !! WILL GIVE BRAINLIEST! Consider the exponential functions f, g, and h, defined as shown. Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval [0, 3].

Answer 1

Answer:

h(x) > f(x) > g(x)

Step-by-step explanation:

Average rate of change of any function 'f' in the interval [a, b] is represented by,

Average rate of change = $\frac{f(b)-f(a)}{b-a}$

1). Average rate of change of f(x) = $16.(\frac{1}{2})^x$ in the interval [0, 3]

Average rate of change = $\frac{16.(\frac{1}{2})^3-16.(\frac{1}{2})^0}{3-0}$

                                        = $\frac{2-16}{3}$

                                        = $-\frac{14}{3}$

                                        ≈ -4.67

2). Average rate of change of g(x) in the interval [0, 3]

  = $\frac{g(3)-g(0)}{3-0}$

  = $\frac{1-27}{3-0}$ [From the table, g(3) = 1 and g(0) = 27]

  = $-\frac{26}{3}$

  ≈ -8.67

3). For the function h(x),

 Average rate of change of the given function h(x),

 = $\frac{h(3)-h(0)}{3-0}$

 = $\frac{-3-4}{3-0}$ [From the graph, h(3) = -3 and h(0) = 4]

 = $-\frac{7}{3}$

 ≈ -2.33

 Since -2.33 > -4.67 > -8.67

 Therefore, decreasing order of the given functions will be,

 h(x) > f(x) > g(x)