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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Mathematics

Ruffles

Today, 08:09

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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Colten Schroeder · 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