Respuesta :
Given:
The table of values of the function f(x).
To find:
How much greater is the average rate of change over the interval [5, 7] than the interval [2, 4]?
Solution:
The average rate of change of a function f(x) over the interval [a,b] is:
[tex]m=\dfrac{f(b)-f(a)}{b-a}[/tex]
The average rate of change over the interval [5, 7] is:
[tex]m_1=\dfrac{f(7)-f(5)}{7-5}[/tex]
[tex]m_1=\dfrac{5002-3452}{2}[/tex]
[tex]m_1=\dfrac{1550}{2}[/tex]
[tex]m_1=775[/tex]
The average rate of change over the interval [2,4] is:
[tex]m_2=\dfrac{f(4)-f(2)}{4-2}[/tex]
[tex]m_2=\dfrac{1048-230}{2}[/tex]
[tex]m_2=\dfrac{818}{2}[/tex]
[tex]m_2=409[/tex]
The difference between the average rate of change over the interval [5, 7] and the interval [2, 4] is:
[tex]Difference=m_1-m_2[/tex]
[tex]Difference=775-409[/tex]
[tex]Difference=366[/tex]
Therefore, the average rate of change over the interval [5, 7] is 366 more than the interval [2, 4].
Answer:
366
Step-by-step explanation:
I took the test lol
