Radioactive substances decay exponentially. For example, a sample of Carbon-14(^{14}C)will lose half of its mass every 5730 years. (In other words, th

Yulia

Yulia

Answered question

2021-05-25

Radioactive substances decay exponentially. For example, a sample of Carbon14(14C)will lose half of its mass every 5730 years. (In other words, the half-life of 14C is 5730 years.) Let A be the initial mass of the sample. Model the decay of  14C using a discrete-time model... (1) using δt=5730 years. (2) using Δt=1year.

Answer & Explanation

aprovard

aprovard

Skilled2021-05-26Added 94 answers

We have:
A initial mass
Half-life of  {4}C is 5730 years
(1)
δt=5730 years
Let m(t) be the mass of the Carbon-14 at 5730-year intervals.
Initinlly, the mass is equal to A.
(0) =A
The mass m(t-1) of 5730 years ago is split in half after one period of 5730 years because the half-life of carbon-14 is 5730 years.
m(t)=m(t1)2 for t>0
Combining these two expressions, we than obtain: m(t)={A if t=0m(t1)2 if t=0 
(2)
δt=1 year
Let m(t) represent the mass of the Carbon-14 after t years.
Initinlly, the mass is equal to A.
m(0) =A
After 5730 years, the mass A is divided by half as the halfife of Carbou-14 is 5730 years.
m(5730)=A2
Combining these two expressions, we then obtain:
 m(t)={A if t=0m(t5730)2 if t=5730x for some positive integer x  Or you could also use the formula m(t)=A(12)t5730 instead (formula for the halfiine), but the book claims that we need to use recurrence relations in this case (which makes is very hard to properly defined it in this case).

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