The goal of this problem set is to remind of the pattern matching skills
that your elementary school teacher tried to teach you. It turns out
that these skills are a prerequisite for being a efficient web site
administrator, computer programmer, analyst, etc. Of course, other
skills needed include reading, writing, and arithmetic.

A car accelerates at 5 meters per square-second like this:

after t = |
0 |
1 |
2 |
3 |
4 |
... |
10 |
... |
15 |
seconds |

it has traveled |
0.0 |
2.5 |
10.0 |
22.5 |
40.0 |
... |
?? |
... |
?? |
meters |

Guess a formula for calculating how far the rock has gotten in t seconds.

Check the formula for the first five table entries. If it doesn't work,
guess more.

Once the formula works for the first five entries, use it and a
calculator or DrScheme's Interactions Window to fill in the two boxes with
?? in the above table.

**Problem 2:**

An older woman suffering from type II diabetes injects insulin based on
measurements of her blood sugar level. If the blood sugar level is less
than 120, she doesn't need to inject any insulin at all. For a value of
120, she injects 1 unit of insulin. For every additional increase of 20 in
her blood sugar level, she gets one additional unit of insulin.

How much insulin does she need to inject for a blood sugar level of 130? 180?

Make a table that shows the number of units of insulin injected for blood
sugar values of 100, 110, 120, ..., 200.

Create a formula for calculating the insulin injections.

Use the formula to determine how many units of insulin the woman needs to
inject for a blood sugar level of 290.

**Problem 3:**

A boy gets retained by a neighborhood association to distribute fliers,
collect dues, and do miscellaneous chores. Just to make sure he is around
when needed, he gets 50 dollars a month (he doesn't have to work for
that). For every hour he works, he gets $8.25.

How much does he get if he works 2 hours? 5 hours? 10 hours? per month.

Make a table that shows the results.

Create a formula for calculating how much the boy earns if he works H hours.

Use the formula and the Interactions Window in DrScheme to find out how
much the boy earns when a major event forces him to work for 100, 132,
and 141 hours in a single month.

**Problem 4:**

A firm wants to pre-print postcard stationary for rejection notices with all
possible combinations of openings. The assumption is that each applicant can be
addressed as either a `Dr.`, `Mr.`, or `Mrs.` followed by a
blank space and followed by a colon (:) or a (,) depending on whether they want
a formal or a friendly rejection notice, respectively.

Figure out and enumerate all possible combinations. Explain how you arrived
at the result.