Show method selection, derivation, conditions, units, verification, and interpretation.
U08 · L04
Name
Date
1
State the central method of Exponential Growth, Decay & Half-Life and list the conditions that must be checked.
Faculty solution: Use deriving and interpreting proportional-rate models. State the relevant hypotheses, domain or interval, units when applicable, and a verification plan.
2
A population doubles in 6 years. Find k.
Faculty solution: k=ln2/6.
3
A substance has half-life 10 days. What fraction remains after 30 days?
Faculty solution: (1/2)^3=1/8.
4
A learner makes an error by ignoring initial conditions, step size, equilibria, or model residuals. Explain the first invalid step and repair the reasoning.
Faculty solution: The first invalid step is ignoring initial conditions, step size, equilibria, or model residuals. Return to the governing definition or theorem, restore the missing condition, and verify the corrected result.
5
Create a short application of Exponential Growth, Decay & Half-Life in population, cooling, mixing, finance, medicine, circuits, and resource systems. Define variables and identify the quantity an integral, differential equation, sequence, or series would measure.
Faculty solution: A defensible response defines variables and units, states assumptions, builds the correct mathematical object, and interprets its value in population, cooling, mixing, finance, medicine, circuits, and resource systems.
6
Describe two independent ways to verify a result from Exponential Growth, Decay & Half-Life.
Faculty solution: Use an exact structural check such as differentiation, substitution, partial sums, or theorem hypotheses; then compare with numerical, graphical, dimensional, or limiting evidence.