Respuesta :
Answer:
6
Step-by-step explanation:
The average rate of change for a function f(x) in the interval a ≤ x ≤ b is given by the formula [tex]\frac{f(b) - f(a)}{b - a}[/tex]
Now, in our case [tex]f(x) = 2^{x} + 10[/tex] and the interval is 2 ≤ x ≤ 4.
So, [tex]f(2) = 2^{2} + 10 = 14[/tex] and [tex]f(4) = 2^{4} + 10 = 16 + 10 = 26[/tex]
Therefore, the rate of change for f(x) over the interval 2 ≤ x ≤ 4 will be
[tex]\frac{f(4) - f(2)}{4 - 2} = \frac{26 - 14}{4 - 2} = 6[/tex]. (Answer)
None of the options is correct.
A rate of change is a rate that describes how one quantity changes in relation to another quantity.
Average rate of change refers to a measure of how much the function changes per unit, on average, over the given interval [tex](a,b)[/tex].
Average rate of change [tex]\boldsymbol{=\frac{f(b)-f(a)}{b-a}}[/tex]
[tex]f(x)=2x+10[/tex]
[tex]f(4)=2(4)+10[/tex]
[tex]=18[/tex]
[tex]f(2)=2(2)+10[/tex]
[tex]=14[/tex]
Average rate of change [tex]\boldsymbol{=\frac{f(4)-f(2)}{4-2}}[/tex]
[tex]=\frac{18-14}{4-2}[/tex]
[tex]=2[/tex]
None of the options is correct.
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