We discuss the analytic view of mathematics such as when and where it is most useful or appropriate.
Analytic perspective is the “down and gritty number crunching” that is often required to support your conclusions. The graphs, charts, and snapshots of progress that are used to convince people in a board room aren’t materialized out of thin air, and they are (usually) not fabricated information. They are the product of hours of effort determining what things to include, what things to exclude, and how the data supports (or doesn’t) the conclusion you are drawing. All of these detailed processes tend to rely on analytic skills.
The most common analytic mathematical tool is algebra. If you wanted to calculate something like a break even point for a company, you wouldn’t draw a graph and guess. Instead you would set the profit equal to zero (or equivalently set the cost equal to the revenue) and solve for time in the resulting equation; utilizing techniques from algebra. This results in a very precise answer. More importantly it is also the same answer anyone else using the same data would yield (assuming no mistakes were made). Thus it is an objective result, once you have established the initial framework of the problem.
Most of our exploration of functions in the coming sections of this course will center around trying to determine/find analytic solutions to geometric observations. Things like “what are the zeros of this function” originate from geometric reasoning but require analytic methods to arrive at a precise conclusion.
We wish to know the population of monkeys in 1962, which would occur at .