Radioactive Decay Beginning with 16 grams of a radioactive element whose half - life is 30 years, the mass y (in grams) remaining after t years is given by

y=23 (1/2) ^t/45, t ≥ 0.

How much of the initial mass remains after 150 years?

Question

Priscilla Harrell

Mathematics

29 November, 15:14

Radioactive Decay Beginning with 16 grams of a radioactive element whose half - life is 30 years, the mass y (in grams) remaining after t years is given by

y=23 (1/2) ^t/45, t ≥ 0.

How much of the initial mass remains after 150 years?

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Answers (1)

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Gringo · Answer 1

the equation should be corrected to fit the data of the problem. With the corrected equation a mass of 0.5 grams remains after 150 years

Step-by-step explanation:

for the mass y (in grams)

y=23 * (1/2) ^ (t/45), t ≥ 0.

the initial mass is at t=0, then

y = 23 grams → should be 16 grams

half-life from the equation = 45 years → should be 30 years

the correct equation should be

y=16 * (1/2) ^ (t/30), t ≥ 0

then after 150 years → t = 150

y=16 * (1/2) ^ (150/30) = 16 * (1/2) ^5 = 16/32 = 0.5 grams

then a mass of 0.5 grams remains after 150 years

Radioactive Decay Beginning with 16 grams of a radioactive element whose half - life is 30 years, the mass y (in grams) remaining after t years is given byy=23 (1/2) ^t/45, t ≥ 0.How much of the initial mass remains after 150 years?

Radioactive Decay Beginning with 16 grams of a radioactive element whose half - life is 30 years, the mass y (in grams) remaining after t years is given by

y=23 (1/2) ^t/45, t ≥ 0.

How much of the initial mass remains after 150 years?