A scientist has a 120 mg sample of an unstable isotope. The amount of the substance remaining in the sample decreases at a rate of 16% each day. At the end of t days, there is less than 30 mg of the substance remaining. Which inequality represents this situation, and after how many days will the sample size remaining be less than 30 mg?

Question

Mathematics

Peyton Beltran

12 February, 11:51

A scientist has a 120 mg sample of an unstable isotope. The amount of the substance remaining in the sample decreases at a rate of 16% each day. At the end of t days, there is less than 30 mg of the substance remaining. Which inequality represents this situation, and after how many days will the sample size remaining be less than 30 mg?

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Answers (1)

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Azul Cohen · Answer 1

After each day there is 1 - 0.16 = 0.84 of the substance left

The inequality is 120*0.84^t < 30

120*0.84^t < 30

0.84^t < 30/120 < 0.25

t * ln 0.84 < ln 0.25

t < ln 0.25 / ln 0.84

t < 7.95

Answer = 8 days