A patient is given a 300mg dose of medicine that degrades by...

A patient is given a 300mg dose of medicine that degrades by 25% every hour. a. Write a function to describe this situation. Identify the units of each value and write a sentence explaining what each piece of the function represents in this context. b. What is the remaining drug concentration after a day? c. Use Guess and Check to determine about how many hours will it take for the drug concentration to be halved. Find an estimated value to the nearest half hour. We want our function to output: ________ Because ______________________________________________________ d. Use Guess and Check to determine about how many hours will it take for the drug concentration reach 5mg. Find an estimated value to the nearest half hour.

Transcript

00:02 Okay, we have a patient that's given a 300 milligram dose of medicine, and it goes down by 25 % each hour.

00:15 All right, so if i'm thinking about that, we're starting with 100%, and then it decreases by 25 % each hour, which means there's 75 % remaining.

00:26 So if i'm writing a function for this, we would say we're starting with 300, and we're going to multiply by 75 % every hour.

00:37 Let's use t for that.

00:39 And since we're talking about kind of a concentration, we can say this is c of t is equal to the following function.

00:49 All right.

00:49 Now, the next piece is what is the remaining drug concentration after a day? so when t is equal to 24, this would be one day.

01:00 So let's plug that in.

01:01 Let's see what we get.

01:02 So we'd have c of 24 is equal to 3 .3 .5.

01:03 So we'd have 3 .4 is equal to 300 and we'd have 0 .75 and we did that 24 different times let's calculate this let's see what we gets a 300 and times 0 .75 to the power 24 and i end up with point 3 remaining to be a little bit more specific 0 .30 milligrams to see at 24 so one day we don't have very much left and i okay, now it says use guess and check to determine how many hours it will take for the concentration to be half.

01:43 So we want to use guess and check.

01:50 Okay, and so we want half of the 300.

01:54 So we want it to be 150.

01:56 Now, we know that 24 hours gives us only 0 .3 remaining.

02:00 So i think maybe a good spot would be like maybe 10.

02:05 And we can check to see where we're at after 10, see if we're close to that 150.

02:10 And what we need to do from there.

02:12 So 300 times 0 .75 to the power 10...