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

Answer:

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

Step-by-step explanation:

Energy of bird flight is given by

$E=429w^{-0.35}$

Differentiating with respect to time we get

$\dfrac{dE}{dt}=429\times -0.35w^{-0.35-1}\dfrac{dw}{dt}\\\Rightarrow \dfrac{dE}{dt}=-150.15w^{-1.35}\dfrac{dw}{dt}$

Now when

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

$\dfrac{dw}{dt}=\text{Rate of change of weight of bird}=0.001\ \text{g/hr}$

$\dfrac{dE}{dt}=-150.15\times 10^{-1.35}\times 0.001\\\Rightarrow \dfrac{dE}{dt}=-0.0067\ \text{cal/g/hr}$

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