Exponential Growth/Decay Explorer — Notebook Template

Explore exponential models y=y0·e^(kt) and y=y0·(1+r)^t, solve for doubling/half-life times, and plot.

graphing exponential models

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What this template does

This is a ready-to-run GetCalcMaster Notebook starter. Open it into Notebook, run once with defaults, then tweak inputs and keep your assumptions next to the math.

How to use it (recommended)

Open in Notebook.
Choose model parameters (k for e^(kt) or r for (1+r)^t).
Compute doubling time or half-life.
Plot y(t) in 2D Graph to validate behavior.
Snapshot parameters and interpretation.

Tip: When a result matters, verify it twice: a unit check + a second method (graph/estimate).

Preview (first cells)

This preview is for readability. The full template loads into Notebook when you click Open.

TEXT

# Exponential Growth / Decay

Two common models:

1) Continuous: **y(t) = y0·exp(k·t)**
- Doubling time (k>0): **t2 = ln(2)/k**
- Half-life (k<0): **t½ = ln(2)/|k|**

2) Discrete: **y(t) = y0·(1+r)^t**

This template uses the continuous form.

MATH

y0 = 100

MATH

k = 0.12  # per time unit; use negative for decay

MATH

t2 = ln(2)/k

MATH

t2

MATH

# Evaluate y at a chosen t
 t = 5
y = y0 * exp(k*t)