SAT Math · Nonlinear functions · hard
A radioactive substance decays by 10% every hour. Starting with 1,000 grams, after how many whole hours does the amount of substance first…
A radioactive substance decays by 10% every hour. Starting with 1,000 grams, after how many whole hours does the amount of substance first drop below 500 grams?
Answer and explanation
Answer: C: 7
After hours, the amount is , because a 10% loss leaves 90%. Compute step by step: after 5 hours, about 590.5 grams; after 6 hours, about 531.4 grams, still above 500; after 7 hours, about 478.3 grams, below 500. So the first whole hour at which the amount is below 500 is 7, choice C. Choice A (5) and choice D (6) are too early, since the sample has not yet dropped below 500. Choice B (10) is too late: it is the correct hour for about 349 grams. A half-life of about 6.6 hours explains the answer.
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