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

Am I on the right track?

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

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

A. This relationship will show exponential decay. Exponential decay occurs when something decreases by a fixed percentage over a given interval of time. In this case, the drug's effectiveness decreases by 20% every hour, which means it decreases exponentially.

B. To 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, we can use the formula for exponential decay.

Let M(t) represent the amount of medication remaining at time t (in hours).

The initial dose given to the patient is 200 mg, so M(0) = 200.

Since the drug's effectiveness decreases by 20% every hour, we can write the equation as:

M(t) = M(0) * (1 - 0.2)^t

Simplifying further, the equation becomes:

M(t) = 200 * (0.8)^t

Therefore, the 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 is M(t) = 200 * (0.8)^t.