Quick questions on Exponential growth and decay: $\frac{dN}{dt} = k N$ , $N = N_0 e^{kt}$ , doubling and half-life

2short 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 continuous compound interest?

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A bank account earning interest at a continuous rate

r

satisfies

\frac{dA}{dt} = r A

, so

A(t) = A_0 e^{r t}

. This is the same model with

N \to A

and

k \to r

What is half-life formula sign?

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T_h = -\frac{\ln 2}{k}

when

k < 0

gives a positive half-life. Using

\frac{\ln 2}{k}

directly would give a negative answer.

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