Question

Find the average rate of change of y=log3⁡ x over the interval 1≤x≤3. Write your answer as a fraction in the simplest form.

Answer 1

Answer:

If the interval is 1 < x < 3, then you are examining the points (1,4) and (3,16). From the first point, let a = 1, and f (a) = 4. From the second point, let b = 3 and f (b) = 16. The average rate of change is 6 over 1, or just 6.

Answer 2

The average rate of change is $\frac{6}{25}$

What is rate of change over an interval?

'When we calculate average rate of change of a function over a given interval, we’re calculating the average number of units that the function moves up or down, per unit along the x-axis. We could also say that we’re measuring how much change occurs in our function’s value per unit on the x-axis.'

According to the given problem,

Rate of change formula = $\frac{f(b) - f(a)}{b-a}$

y = log3x

⇒ a= 1

   b= 3

Therefore,

⇒ $\frac{log(3*3) - log(3*1)}{3-1}$

⇒ $\frac{log9 - log3}{2}$

⇒$\frac{1}{2}$ log$(\frac{9}{3})$

⇒ $\frac{1}{2}$ * log 3

⇒ $\frac{6}{25}$

Hence we can conclude the rate of change as $\frac{6}{25}$

Learn more about rate of change here: https://brainly.com/question/18193470

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