emblemhacks
01.08.2020 •
Mathematics
A radioactive substance is decaying exponentially. If there are initially 15 grams of the substance and after 3 hours there are 5 grams, what is the approximate half life of the substance, in hours? Round to two decimal places.
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Ответ:
Ok, an exponential decay is written as:
P(t) = A*(1 - r)^t
Where A is the initial population, r is the rate of decay and t is the unit of time.
We know that the initial population is 15g
then:
P(t) = 15g*(1 - r)^t
And at t = 3hs, the populations is 5g
P(5h) = 5g = 15g*(1 - r)^5
5/15 = 1/3 = (1 - r)^5
(1/3)^(1/5) = (1 - r) = 0.8
Now, the half life time of the sustance is t = x, such that the population reduces to it's half:
P(x) = A/2 = 15g/2 = 7.5g
Then:
7.5g = 15g*0.8^x
7.5g/15g = 1/2 = 0.8^x
Now, remember that if we have:
a = b^x
then
x = ln(a)/ln(b)
ln(1/2)/ln(0.8) = x = 3,11 hours
Ответ:
49
Step-by-step explanation: no idea i just evaluated like that