Question

These tables represent an exponential function. Find the average rate of change for the interval from x=9 to x=10

Answer 1

ANSWER

B. 39,366

EXPLANATION

The y-values of the exponential function has the following pattern

${3}^{0} = 1$

${3}^{1} = 3$

${3}^{2} = 9$

${3}^{3} = 27$

:

:

${3}^{x} = y$

Or

$f(x) = {3}^{x}$

To find the average rate of change from x=9 to x=10, we simply find the slope of the secant line joining (9,f(9)) and (10,f(10))

This implies that,

$slope = \frac{f(10) - f(9)}{10 - 9}$

$slope = \frac{ {3}^{10} - {3}^{9} }{1}$

$slope = \frac{59049-19683}{1} = 39366$

Therefore the average rate of change from x=9 to x=10 is 39366.

The correct answer is B.

Answer 2

Answer:

Hi there!

The answer to this question is: B

Step-by-step explanation:

The function for the question is: y=3^x

3^10=59049 and 3^9=19683

Then you just subtract the two numbers to get 39366