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Mila [183]
4 years ago
15

Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 4%. If the rate of deca

y is proportional to the amount of the substance present at time t, find the amount remaining after 24 hours. (Round your answer to one decimal place.)
Mathematics
1 answer:
11111nata11111 [884]4 years ago
5 0

Answer:

84.96 mg

Step-by-step explanation:

No = 100 mg

t = 6 hours, N = 96% of No = 96 / 100 No

t = 24 hours, N = ?

Let after 24 hours the remaining part is N.

Use the decay law equation

N = No e^-λt

96 / 100 = e^-6λ  

0.96 = e^-6λ

taking natural log on both the sides

ln 0.96 = - 6λ

λ = 6.8 x 10^-3 per hour

Now,

N = No e^-24λ

N = No x e^-(24 x 6.8 x 10^-3)

N = No (0.8496)

N = 100 x 0.8496 = 84.96 mg

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