rebecca101
contestada

The sequence an = one half(2)n − 1 is graphed below:

coordinate plane showing the points 2, 1; 3, 2; 4, 4; and 5, 8

Find the average rate of change between n = 2 and n = 4.

three halves
two thirds
2
3
Please someone help me. Thank you.

Respuesta :

apologiabiology
your thing is very confusign

anyway, all I need to know to find the average rate of change from n=2 to n=4 is the value of (2,f(2)) and (4,f(4))

we see that the points are (2,1) and (4,4)
the average rate of change from n=2 to n=4 is the slope from (2,1) to (4,4)

slope between (x1,y1) and (x2,y2) is (y2-y1)/(x2-x1)
so slope between (2,1) and (4,4) is (4-1)/(4-2)=3/2
the slope is 3/2 or three halves


answer is three halves

Answer:

option A is correct

three halves i.e, [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

Average rate of Change(A(x)) of f(x) over interval [a, b] is given by:

[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex]

As per the statement:

The sequence is given as:

[tex]a_n =\frac{1}{2} \cdot (2)^{n-1}[/tex]

To find the average rate of change between n = 2 and n = 4.

From the coordinate plane:

At n =2

[tex]a_2 = 1[/tex]

and

at n = 4

[tex]a_4 = 4[/tex]

Now, using average formula we have;

[tex]A(n) = \frac{a_4-a_2}{4-2}[/tex]

⇒[tex]A(n) = \frac{a_4-a_2}{2}[/tex]

Substitute the given values we have;

[tex]A(n) = \frac{4-1}{2} =\frac{3}{2}[/tex]

therefore, the average rate of change between n = 2 and n = 4 is, [tex]\frac{3}{2}[/tex]

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