Certain chemotherapy dosages depend on a patient's surface...

Certain chemotherapy dosages depend on a patient's surface area. According to the Mosteller model, S = ?(hw) / 60, where h is the patient's height in centimeters, w is the patient's weight in kilograms, and S is the approximation to the patient's surface area in square meters. Assume that Kim's height is a constant 166 cm, but she is losing weight. If she loses 6 kg per month, how fast is her surface area decreasing at the instant she weighs 70 kg? Use implicit differentiation to determine dS/dt when Kim's height is a constant 166 cm. dS/dt = ?(166) / (120?(w)) * dw/dt If she loses 6 kg per month, Kim's surface area is decreasing by [ ] m² / month at the instant she weighs 70 kg. (Round to four decimal places as needed.)

Transcript

00:01 Hi there.

00:02 So for this problem, we are told that certain chemotherapy dosages depend on a patient's surface area.

00:09 According to the most stellar model, the surface ms, which is the approximation to the patient's surface area, is equal to the square root of the product between the patient's height and the patient's weight, and this divided by 60.

00:31 So with that said, we are told to assume that kim's height is a constant, so the height is always...

00:38 Oh sorry, well the height...

00:43 Well let me write again this in here.

00:46 This divided by 60 and the height is a constant, right? but well, it is given in centimeters, so that will be 166 centimeters, this in meters, and we just divide that by 100, so that will give us 1 .66 meters.

01:10 And then...

01:11 But she's losing weight, okay? now if she loses 6 kilograms per month, so we are given the rate of change of the weight with respect to time, this should be negative because it is decreasing, okay? so that will be minus 6 kilograms per month, right? and then the question is, how fast is her surface area decreasing? so that will be the rate of change of the surface area with respect to time.

01:37 We don't need to put the negative because we are already told that it's decreasing, okay? and at the instance that she weights, when the weight is equal to 17.

01:48 Now, the thing that we need to do in here is to take the surface area expression that we are given and divide both sides of that with respect to the weight because that is the only one that...

02:07 Well, with respect to the time, okay? both sides of this.

02:11 So we will have the rate of change of the surface area with respect to time is just equal to...

02:17 We can separate this as follows, we can write this as the square root of the height times the square root of the weight, then this divided by 16.

02:28 So if we divide the height, we will obtain that, we will obtain a 1 divided by 2 because remember that we can write this as the weight elevated to 1 divided by 2...

Question

Please give Ace some feedback