Thread: How to derive piecewise function?

The problem statement, all variables and given/known data

A table with Amy's weekly expenditure is given below:

Day 1: $153
Day 2: $119
Day 3: $103
Day 4: $98
Day 5: $99
Day 6: $83
Day 7: $153
Day 8: $202
Day 9: $218
Day 10: $225
Day 11: $219
Day 12: ?

(a) Express Amy's daily expenditure from Day 1 to Day 11 as a piecewise function. Plot the piecewise function graph.
(b) Using the piecewise function, estimate her expenditure for Day 12.
(c) What are the assumptions made in part (b)?


The attempt at a solution

I've been trying to figure this question out for the past few days but just couldn't understand how to go about doing it, even after reading website after website about piecewise functions.

In the end I tried plotting the values in excel, and obtained this graph:


So I assume that the 3 parts that I boxed up in red are the three parts of the piecewise graph? Or not? I'm really clueless D:

Can anyone help me in deriving the piecewise function from the table of values and how to plot the graph from there? I think I'll be able to do parts (c) and (d) of the question once I get pass part (a).

Any help is much appreciated!
Thanks!

I believe the piecewise function is supposed to have 1 "piece" for each data interval. So, there would be 10 pieces given.