Quick questions on Exponential growth and decay: dN/dt = kN, Newton's law of cooling and applications

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is fitting a model to data?

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A typical exam question gives you the initial value and one further data point, and asks you to fit the model. The recipe is fixed:

What is half-life?

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For decay with rate constant

k < 0

, the half-life is

\tau = \frac{\ln 2}{|k|}

. Equivalently

N(t) = N_0 \cdot (1/2)^{t / \tau}

What is wrong sign of

k

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For decay and cooling,

k

is negative. The exponent

k t

should drive the function towards its limit, not away from it.

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