# 9. When doctors prescribe medicine, they must consider how much the drug’s effectiveness will decrease as time passes. If each hour a drug is 20% less effective as the previous hour, at some point the patient will not be receiving enough medicine and must be given another dose.

A. Will this relationship show exponential growth or decay? Explain your reasoning.

B. A patient was given an initial dose of 200 mg of medication. Write an equation that shows the relationship between the amount of medication remaining in the patient’s bloodstream, and the time in hours, , since the medication was administered.

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1. The first one is a decay because the drug is getting less effective each hour.

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2. Am I on the right track?

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3. Can you help me figure out the equation I'm not really sure about it

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4. since 20% less effective each hour, that means that its effectiveness is 80% as much, and that repeats every hour. So, after x hours, the effectiveness is

y = 0.8^x

So, yes, it is exponential, and yes, it is decay.

For B, since the initial dose is 200 mg, the amount left after x hours is

y = 200*0.8^x

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