8 Exponential Growth and Decay Packet - Parkway C-2 - pkwy k12 mo 2025

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The exponential decay formula is used to find the population decay, half-life, radioactivity decay, etc. The general form is f(x) = a (1 - r)x.
The half-life of a radioactive isotope is the time it takes for half the substance to decay. Given the basic exponential growth/decay equation h(t)=abt, half-life can be found by solving for when half the original amount remains; by solving 12a=a(b)t, or more simply 12=bt.
Remember that the original exponential formula was y = abx. You will notice that in these new growth and decay functions, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r). The growth rate (r) is determined as b = 1 + r.
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