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Serga [27]
3 years ago
10

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

Mathematics
2 answers:
viktelen [127]3 years ago
7 0

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}

Verizon [17]3 years ago
6 0

Answer:  2048

<u>Step-by-step explanation:</u>

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

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