Question

the number of users on a new social media website can be modeled by the function f(t) = 12(1.2)^t , where t is the time, in weeks, since the site was launched. Find and interpret the average rate of change on the interval (3,6) round to the nearest whole number

Answer 1

The number of users on new social media site increase as 21, 25, 30, 36,
The average rate of change is given by 5.

The function f (t) = 12 (1.2) ^t show how the rate of users increases in weeks.

What is Average?

Average of the values is the ratio of total sum of values to the number of values.

Here,  f (t) = 12 (1.2) ^t is defined in the range of (3, 6)
So the value of the function in its range is given by
1)  f (3) = 12 (1.2) ^3
          = 21
2)  f (4) = 12 (1.2) ^4
   =  25
3)   f (5) = 12 (1.2) ^5
    = 30
4)   f (6) = 12 (1.2) ^6
     = 36
Now the average rate of change = sum of all difference in values at every week / max. Difference in interval of range(3,6)

= f(6)-f(3)/6-3
= 15/3
= 5

Thus required average change of rate is 5.

Learn more about average here:

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