te^-3t sin4t

Answered question

2022-04-29

te^-3t sin4t

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-05-02Added 556 answers

To solve this problem, we can use the equation for radioactive decay:
N(t)=N0eλt
where N(t) is the amount of radioactive substance at time t, N0 is the initial amount, λ is the decay constant, and t is time.
We know that the half-life T1/2 of the substance is 240 days. This means that after one half-life, the amount of substance remaining will be half of the initial amount:
N(240)=12N0
We can rearrange this equation to solve for the decay constant:
λ=ln2T1/2
Substituting the given values, we get:
λ=ln22400.00289 day1
Now we can use this value of λ to find how long it will take for the sample to decay from 100 mg to 98 mg:
N(t)=N0eλt
Substituting N0=100 mg and N(t)=98 mg, we get:
98=100e0.00289t
Dividing both sides by 100 and taking the natural logarithm of both sides, we get:
ln(98100)=0.00289t
Simplifying, we get:
t239.8 days
Therefore, it will take approximately 239.8 days for the sample to decay from 100 mg to 98 mg with a half-life of 240 days.

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