1. The rate of medication being metabolized in the human body is assumed to be pro- portional to the quantity of medication - that is, y' = ky. Eliot drinks a cup of coffee during lunch (and does not consume any additional caffeine afterwards). At 1pm, they have 100 milligrams of caffeine in their bloodstream to be metabolized. If half of the caffeine is still present after 5 hours, how much caffeine is still in Eliot's bloodstream at 9pm? Answers should be left in terms of exponentials, logarithms, and other calculator func- tions as necessary.

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