A patient is given 2 mg of morphine to control pain. About...

A patient is given 2 mg of morphine to control pain. About 31% of any morphine in the blood is washed out every hour. (a) Construct a function that models the level M of morphine (in mg) in the blood t hours after one dose. M = (b) How much morphine (in mg) remains in the blood after 3 hours? (Round your answer to two decimal places.) mg (c) Estimate how long, in hours, it will take for the amount of morphine left to drop to 0.1 mg. (Round your answer to two decimal places.) h

Transcript

00:01 Okay, so to answer this question, i want you to think of a compound interest calculator.

00:15 But in this case, the value is not going up, but it's going down.

00:21 So this is how to respond to the first question.

00:25 This is how you're going to be going to set it up.

00:29 So it's gonna it's gonna look like i'm sure you know what a compound interest is but instead of minus instead of plus it's gonna be minus because it's going down value so we're gonna say the muffin the other left will be two parentheses one minus the rates which is 31 % which is 0.

01:00 31 with the time so that would be the function and where this came from it came from your the compound equate the compound interest equation which is kind of that's something a equals p parenthesis 1 minus rates over it and parenthesis n parentheses n but in this case, you're not going to worry about this.

01:36 You're just going to worry about the time and the rates.

01:39 And p is where you see the principle.

01:41 This is where you start from.

01:43 But that's how we derive this function using the compound interest equation.

01:54 But usually the compound interest equation is always plus because this is going down.

02:00 We're going to use minus.

02:02 That's going to be the answer for the first one so m equals to parenthesis 1 minus 0 .3 1 c is the time we're we're talking about here now the next second question here is how many muffin will be left after three hours all you have to do do is just to change your t this t to three that's all you have to do and what do we do set this up m equals two times one minus zero point thirty one and in this case the t is what three and all you have to do when you plug this into your calculator, you will end up with two parentheses.

03:12 You have to follow your pemdas.

03:15 1 minus 0 .31.

03:18 We give you 0 .69 cube...

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