Question

the energy cost of a bird flight as a function of body weightis given by: E=429w^-0.35 where w is the weight of the bird in g and E is the energyexpenditure in cal/g/hr. Suppose that the weight of a bird weighing10 g is increasing at a rate of 0.001 g/hr. Find the rate at whichthe energy expenditure is changing with respect to time.

Answer 1

The rate at whichthe energy expenditure is changing with respect to time is -0.00671 cal/g/hr².

Explanation:

We know that:

`E=429w^(-0.35)`

`(dw)/(dt) =0.001`

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:

`(dE)/(dt)=(dE)/(dw)\cdot (dw)/(dt)`

We have to calculate dE/dw

`(dE)/(dw)=429*(-0.35)*w^(-0.35-1)=-150.15w^(-1.35)`

Then

`(dE)/(dt)=(dE)/(dw)\cdot (dw)/(dt)=-150.15w^(-1.35)*0.001=-0.15015w^(-1.35)\\\\(dE)/(dt)_(w=10)=-0.15015*(10)^(-1.35)= -0.15015*0.04467 =-0.00671`

The rate at whichthe energy expenditure is changing with respect to time is -0.00671 cal/g/hr².