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For an exponential function:

General equation of exponential decay is A(t)=A0e^-at

The definition of a half-life is A(t)/A0=0.5, therefore:

0.5 = e^-at

ln(0.5)=-at

t= -ln(0.5)/a

For exponential growth: A(t)=A0e^at

Find out an expression to relate A(t) and A0 and you solve as above

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Q: How can you use logarithmic and exponential equations and properties to solve half-life and logistic growth scenarios?
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