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.

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boffeemadrid boffeemadrid · Answer 1 · 2020-10-31T14:27:49+01:00

Answer:

[tex]-0.0067\ \text{cal/g/hr}[/tex]

Step-by-step explanation:

Energy of bird flight is given by

[tex]E=429w^{-0.35}[/tex]

Differentiating with respect to time we get

[tex]\dfrac{dE}{dt}=429\times -0.35w^{-0.35-1}\dfrac{dw}{dt}\\\Rightarrow \dfrac{dE}{dt}=-150.15w^{-1.35}\dfrac{dw}{dt}[/tex]

Now when

[tex]w=\text{Weight of bird}=10\ \text{g}[/tex]

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

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

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