Bethany subscribes to an on-demand media provider, Netplay. With each bill she p

Question

Bethany subscribes to an on-demand media provider, Netplay. With each bill she pays a one time fee of $7 for the subscription and then pays $4 per movie she watches. a. Complete the table below by determining the average rate of change of the cost of Bethany's bill with respect to the number of movies she has watched The change in the Number of number of moviesovies B Bethany has Bethany watched,Ak | watches, k The average rate of The change in change of the cost of Cost of the cost of Bethany's bill with Bethany's bill Bethany's bill, respect to the number (in dollars), p | p (in 1 of movies she has dollars) watched (in dollars per number of movies) b. Define a function t that gives the cost of Bethany's bill (in dollars) in terms of the number of movies Bethany has watched, A 7 4 Preview c. Using the table above, what do you notice about the average rate of change of the cost of Bethany's bill with respect to the number of movies she has watched for consecutive equal changes in the number of movies she has watched? The average rate of change of the cost of Bethany's bill with respect to the number of movies she has watched is increasing O The average rate of change of the cost of Bethany's bill with respect to the number of movies she has watched is constant The average rate of change of the cost of Bethany's bill with respect to the number of movies she has watched is at first increasing then decreasing The average rate of change of the cost of Bethany's bill with respect to the number of movies she has watched is decreasing. None of the above d. Use function notation to represent the change in the cost of Bethany's bill as the sumber of movies Bethany has watched increases from 9 to 15.

Explanation / Answer

Change in number of movies (delta k)

a. Please refer to the above completed table

b. From the above table, delta p / delta k = 4

Let us say initial p and k are some fixed p1 and k1,

Then we have (p - p1) / (k - k1) = 4

or p = 4k + c, where c is some constant ...........(1)

Plugging in the value of p from the table, for k = 2 in the equation (1)

15 = 4*2 + c

c = 7

Hence equation (1) must be

p = 4k + 7

Change in number of movies (delta k)

Number of movies (k) Cost in dollars (p) Change in cost (delta p) Average rate of change (delta p/ delta k) - 0 7 - - 2 (=2-0) 2 15 (=7+[2*4]) 8 (=15-7) 4 (=8/2) 2 (=4-2) 4 23 (=7+[4*4]) 8 (=23-15) 4 (=8/2) 2 (=6-4) 6 31 (=7+[6*4]) 8 (=31-23) 4 (=8/2)

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