Answer:
The rate at whichthe energy expenditure is changing with respect to time is -0.00671 cal/g/hr².
Step-by-step explanation:
We know that:
[tex]E=429w^{-0.35}[/tex]
[tex]\frac{dw}{dt} =0.001[/tex]
In this case we have to apply the the Chain Rule to derive the functions.
We want to to know the rate of change of the energy expenditure E with respect to time (dE/dT).
Applying the chain rule:
[tex]\frac{dE}{dt}=\frac{dE}{dw}\cdot \frac{dw}{dt}[/tex]
We have to calculate dE/dw
[tex]\frac{dE}{dw}=429*(-0.35)*w^{-0.35-1}=-150.15w^{-1.35}[/tex]
Then
[tex]\frac{dE}{dt}=\frac{dE}{dw}\cdot \frac{dw}{dt}=-150.15w^{-1.35}*0.001=-0.15015w^{-1.35}\\\\\frac{dE}{dt}_{w=10}=-0.15015*(10)^{-1.35}= -0.15015*0.04467 =-0.00671[/tex]
The rate at whichthe energy expenditure is changing with respect to time is -0.00671 cal/g/hr².
