half-life question for math?

Question

half-life of a certain radioactive substance is 14 days. there are 6.6grams presnt initially.

what is the rate of decrease?
what is the growth factor?(can u also tell me what that means, thanks)

Answer 1

P(t)=Poe^(-kt)

P(t) is the material at time t, Po is the initial material present, k is the growth factor and t is time. It's minus k because this is decay.

first, let's find the growth factor k, k has units of 1/time, in this case it's 1/day. the product kt needs to be unit-less.

at 14 days we have half of the material so
P(14)/Po=1/2=e^(-14k) solving for k we get k=0.0495

so P(t)=6.6e^(-0.0495t)

rate of decrease=dP/dt=-0.0495*6.6e^(-0.0495t)=
-0.3268e^(-0.0495t).
The instantaneous rate of decrease depends on which time you select.