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.
