   Chapter 14.3, Problem 94E

Chapter
Section
Textbook Problem

The average energy E (in kcal) needed for a lizard to walk or run a distance of 1 km has been modeled by the equation E ( m , v ) = 2.65 m 0.66 + 3.5 m 0.75 v where m is the body mass of the lizard (in grains) and v is its speed (in km/h). Calculate Em(400, 8) and Ev(400, 8) and interpret your answers.

To determine

To calculate: The values of Em(400,8) and Ev(400,8) using the given function E(m,v)=2.65m0.66+3.5m0.75v and interpret these values.

Explanation

Given:

The function is, E(m,v)=2.65m0.66+3.5m0.75v , where m is mass (in grams) and v is speed (in km/h).

Calculation:

The given function is, E(m,v)=2.65m0.66+3.5m0.75v .

Take the partial derivative with respect to m and obtain Em .

Em=m(2.65m0.66+3.5m0.75v)=m(2.65m0.66)+m(3.5m0.75v)=2.65m(m0.66)+3.5vm(m0.75)=2.65(0.66)m0.34+3.5v(0.75)m0.25

Thus, Em=1.749m0.34+2.625m0.251v . (1)

Substitute m=400 and v=8 in the equation (1) and obtain the value of Em(400,8) ,

Em=1.749(400)0.34+2.625(400)0.2518=1.749(0.1304)+2.625(0.2236)(18)=0.2281+0

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