Question

These tables represent an exponential function.Find the average rate of change for the interval from x=8 to x=9

Answer 1

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 $T_{n}=ar^{n-1}$

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

$T_{9}=2.3^{9-1}=2.3^{8}$

T9 = 13122

Therefore Option D. 13122 will be the answer.