Question

Which expression below gives the average rate of change of the function h(x)=4^(x+2)+7 on the interval –3 ≤ x ≤ 5?

Answer 1

Answer:

$\frac{4^8-1}{32}$

Step-by-step explanation:

$h(x)=4^{(x+2)} +7$

We know that formula for average rate of change of a function from a to b is

$\frac{f(b)-f(a)}{b-a}$

Here f equals h and a =-3 b=5

h(a) = $4^{5+2} +7 = 4^7+7$

and

h(b) = $4^{-3+2} +7 = \frac{1}{4} +7$

h(b)-h(a) =$4^7-\frac{1}{4} =\frac{4^8-1}{4}$

b-a = 5-(-3) =8

Hence average rate of change is

$\frac{4^8-1}{4}(\frac{1}{8} )=\frac{4^8-1}{32}$

Answer 2

Answer:  2048

Step-by-step explanation:

h(x) = 4ˣ⁺² + 7

                        h(5) = 4⁵⁺² + 7

                               = 4⁷ + 7

                                                    h(-3) = 4⁻³⁺² + 7

                                                             = 4⁻¹ + 7

Average rate of change is the slope of the interval.

$\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{h(5)-h(-3)}{5 - (-3)}=\dfrac{(4^7+7)-(4^{-1}+7)}{5 + 3} = \dfrac{16391-7.25}{8}=2048$