The brain mass of a fetus can be estimated using the total...

The brain mass of a fetus can be estimated using the total mass of the fetus by the function b = 0.22m^0.87, where m is the mass of the fetus (in grams) and b is the brain mass (in grams). Suppose the brain mass of a 30 g fetus is changing at a rate of 0.23 g per day. Use this to estimate the rate of change of the total mass of the fetus, dm/dt. dm/dt = g per day (Round to five decimal places as needed.)

Transcript

00:01 Hi there, so for this problem, we are told that the brain mass of a fetus can be estimated using the total mass of the fetus by the function that is given.

00:10 And that function is that b is equal to 0 .22 times the mass elevated to 0 .87.

00:23 And we are given that the rate of change of b, that is the derivative of b with respect to time, equal to 0 .23 grams per day.

00:45 0 .23 grams per day.

00:55 And the other information that we are given in this case is that the value of b at this is 30.

01:08 Okay, so the value of b is 30 grams.

01:13 So what we need to obtain from this is the change of the total mass of the fetus.

01:25 So that will be the rate of change of the mass with respect to time.

01:29 So that was what we need to obtain in here.

01:31 So to obtain this expression first, we need to derive the expression for b that we are given with respect to the time.

01:39 So we will have the derivative of b with respect to time is equal to 0 .22.

01:47 We take down the exponent and that will be the mass times elevated to 0 .87 minus 1 and this times the rate of change of the mass with respect to time.

02:02 Now with that said we just need to simply solve for this for this expression right here.

02:12 So let me just use my calculator to reduce or simplify this in here.

02:24 So in here, 0 .22 times 0 .8 is equal to 0 .14.

02:51 And the other term in here is the mass elevated to.

03:01 So we will have the mass elevated to minus 0 .13...

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