These tables represent an exponential function.Find the average rate of change for the interval from x=8 to x=9
1 answer:
Answer:
Option D. 13122 is the answer.
Step-by-step explanation:
As we can see from the table having interval and average rate of change, figures under average rate of change are forming a geometric sequence.
Sequence is 2, 6, 18 , 54, 162, 486.
and we have to find the average rate of change from x = 8 to x = 9, means we have to find 9th term of the given sequence.
Now we know that explicit formula of the sequence can be written as
where Tn is the nth term of the sequence.
a = first term
r = common ratio
n = number of the term
Now from this explicit formula we can find the 9th term of the sequence.
From the given table
a = 2, r = 3, n = 9
T9 = 13122
Therefore Option D. 13122 will be the answer.
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Now look at the smaller right angled triangle (LMJ)
Hypotenuse is the line LJ which is
The adjacent angle is 45
Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h
therefore
x= * sin45= 4
The triangle KJL (big right angled triangle) has been given the following dimensions
Hypotenuse =
The adjacent angle is 30 degrees
Since we have the hypotenuse and the angle we must use the equation
opposite = Sin(angle) x Hypotenuse
Opposite= sin30 x
Opposite=
Therefore line LJ is
Now look at the smaller right angled triangle (LMJ)
Hypotenuse is the line LJ which is
The adjacent angle is 45
Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h
therefore
x=