A first quantitative lesson

A simple relationship

Many scientific relationships can first be explored with a small model. The illustration below shows the three parts of the workflow used in this lesson.

Observe a system, express a model, and interpret its result.

Suppose a measured response is proportional to an input:

\[ y = kx. \]

The optional supporting package can keep reusable calculations in one tested place while the course page concentrates on interpretation.

from course_utils.example import proportional_response

inputs = [0, 1, 2, 3]
[(value, proportional_response(value, rate=2.5)) for value in inputs]

Table 1: Responses predicted by a proportional model.

[(0, 0.0), (1, 2.5), (2, 5.0), (3, 7.5)]

Exercise

Predict the response for an input of 4 when \(k=2.5\). Explain what the value of \(k\) means in this model.

# Replace the missing value, then run the cell.
proportional_response(4, rate=...)

Takeaway

A useful computational example should support the scientific idea rather than hide it. Put reusable mechanics in a helper only when that makes the authored lesson clearer.