Question

The energy of bird flight as a function of body weight is given by, E = 429 w−0.35, where w is the weight of the bird (in g) and E is the brain weight (in cal/g/hr). Suppose that the weight of a bird weighing 10 g is increasing at a rate of 0.001 g/hr. Find the rate at which the energy expenditure is changing with respect to time in cal/g/hr/hr to four decimal places.

Answer 1

`-0.0067\ \text{cal/g/hr}`

Explanation:

Energy of bird flight is given by

`E=429w^(-0.35)`

Differentiating with respect to time we get

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

Now when

`w=\text{Weight of bird}=10\ \text{g}`

`(dw)/(dt)=\text{Rate of change of weight of bird}=0.001\ \text{g/hr}`

`(dE)/(dt)=-150.15* 10^(-1.35)* 0.001\\\Rightarrow (dE)/(dt)=-0.0067\ \text{cal/g/hr}`

The rate at which the energy expenditure is changing with respect to time is
`-0.0067\ \text{cal/g/hr}`