Question

Angela painted 4 pictures in 7 days. She paints additional pictures at the rate of 1 per day. Which recursive function gives the total number of pictures she will have painted at any day in the future? How many pictures will she have painted if she paints for another 5 days after the initial week?

Answer 1

The recursive function that gives the total number of pictures she will have painted at any day in the future is

next = now + 1, starting at 4 , and the total number of pictures after a week plus 5 days is 9.

.

Explanation:

Answer 2

The recursive function gives the total number of pictures Angela will have painted at any day in the future is:

• PP(t) = t +
  `(4)/(7)t`

The number of pictures will she have painted if she paints for another 5 days after the initial week is:

• 18.86

Explanation:

To obtain the recursive function, you must take into account the next:

1. Angela paints 4 pictures in 7 days, by this, you can say Angela paints 4/7 of a picture by day.

2. Angela paints additional 1 picture by day, with this, the number of pictures painted additionally is equal to the time t (because 1 day = 1 picture, 2 days = 2 pictures and so on). With the data taken into account, we can elaborate the next function:

• PP(t) = t +
  `(4)/(7)t`

Where:

• PP: Painted pictures.

• t: time in days.

For example, if you need to know how many pictures she painted in the first week, you can calculate replacing t by 7:

• PP(t) = t +
  `(4)/(7)t`
• PP(7) = 7 +
  `(4)/(7)*7`
• PP(7) = 7 + 4
• PP(7) = 11

If she paints for another 5 days (I mean 12 days taking into account the initial week), we can calculate:

• PP(t) = t +
  `(4)/(7)t`
• PP(12) = 12 +
  `(4)/(7)*12`
• PP(12) = 12 +
  `(48)/(7)`
• PP(12) =
  `(132)/(7)`
• PP(12) = 18.86

To the day 12, Angela will paint 18.86 pictures.