Question

The brain mass of a fetus can be estimated using the total mass of the fetus by the function b equals 0.22 m superscript 0.87b=0.22m0.87?, where m is the mass of the fetus? (in grams) and b is the brain mass? (in grams). suppose the brain mass of a 2323?-g fetus is changing at a rate of 0.240.24 g per day. use this to estimate the rate of change of the total mass of the? fetus, startfraction dm over dt endfraction dm dt.

Answer 1

We are given
b = 0.22 m^0.87
db/dt = 0.24 g/day at b = 23 g

where
b is the brain mass of the fetus
m is the total mass of the fetus
db/dt is the rate of change of the brain mass of the fetus

We are asked to get the rate of change of the total mass of the fetus

First, we take the first derivative of the given equation with respect to time
db/dt = 0.22 (0.87) m^(0.87-1) dm/dt
Next, simplify and substitute the given values. So,
0.24 g/day = 0.22(0.87)(23)^(0.87 -1 ) dm/dt
Solving for dm/dt
dm/dt = 1.88 g/day

The rate of change of mass of the fetus is 1.88 g/day.