Applications

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Many real situations are modeled by the differential equation $y^{'} = k y$ , where $k$ is a constant. Its solution is $y (t) = y_{0} e^{k t}$ , with $y_{0}$ the initial value. If $k > 0$ , the quantity grows exponentially; if $k < 0$ , it decays exponentially. To use it, identify the rate of change, write $y^{'} = k y$ , find $k$ from given data, and substitute the initial condition.

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Curated

#	Title	Difficulty	Tags
176	Carbon dating	Easy	Half-lifeExponential decay
412	Falling for two seconds	Easy	Applications
414	A capacitor discharges	Easy	Applications
415	Continuous compounding	Easy	Applications
416	Terminal velocity	Easy	Applications
418	A drug's rate constant	Easy	Applications
419	Cooling for ten minutes	Easy	Applications
420	A pendulum's period	Easy	Applications

From open sources

Complete problems only, with worked solutions first. Show everything

#	Title	Difficulty
133574	How often should a drug be taken if its dose is 3…	Easy
133576	The actual elimination of nicotine is multiexponential:	Easy