Chapter 9.3, Problem 51E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

*Allometric growth* in biology refers to relationships between sizes of parts of an organism (skull length and body length, for instance). If *L*_{1}(*t*) and *L*_{2}(*t*) are the sizes of two organs in an organism of age *t*, then *L*_{1} and *L*_{2} satisfy an allometric law if their specific growth rates are proportional:

where *k* is a constant.

(a) Use the allometric law to write a differential equation relating *L*_{1} and *L*_{2} and solve it to express *L*_{1} as a function of *L*_{2}*.*

(b) In a study of several species of unicellular algae, the proportionality constant in the allometric law relating *B* (cell biomass) and *V* (cell volume) was found to be *k* = 0.0794. Write *B* as a function of *V.*

(a)

To determine

**To solve:** The solve the given function:

Explanation

**Given:**

*t.*

The allometric function is,

**Calculation:**

The function can be written as follows,

Integrate on both sides,

(b)

To determine

**To find:** The function

Sect-9.1 P-1ESect-9.1 P-2ESect-9.1 P-3ESect-9.1 P-4ESect-9.1 P-5ESect-9.1 P-6ESect-9.1 P-7ESect-9.1 P-8ESect-9.1 P-9ESect-9.1 P-10E

Sect-9.1 P-11ESect-9.1 P-12ESect-9.1 P-13ESect-9.1 P-14ESect-9.1 P-15ESect-9.1 P-16ESect-9.1 P-17ESect-9.2 P-1ESect-9.2 P-2ESect-9.2 P-3ESect-9.2 P-4ESect-9.2 P-5ESect-9.2 P-6ESect-9.2 P-7ESect-9.2 P-8ESect-9.2 P-9ESect-9.2 P-10ESect-9.2 P-11ESect-9.2 P-12ESect-9.2 P-13ESect-9.2 P-14ESect-9.2 P-19ESect-9.2 P-20ESect-9.2 P-21ESect-9.2 P-22ESect-9.2 P-23ESect-9.2 P-24ESect-9.2 P-27ESect-9.3 P-1ESect-9.3 P-2ESect-9.3 P-3ESect-9.3 P-4ESect-9.3 P-5ESect-9.3 P-6ESect-9.3 P-7ESect-9.3 P-8ESect-9.3 P-9ESect-9.3 P-10ESect-9.3 P-11ESect-9.3 P-12ESect-9.3 P-13ESect-9.3 P-14ESect-9.3 P-15ESect-9.3 P-16ESect-9.3 P-17ESect-9.3 P-18ESect-9.3 P-19ESect-9.3 P-20ESect-9.3 P-21ESect-9.3 P-22ESect-9.3 P-23ESect-9.3 P-24ESect-9.3 P-29ESect-9.3 P-30ESect-9.3 P-31ESect-9.3 P-32ESect-9.3 P-33ESect-9.3 P-34ESect-9.3 P-35ESect-9.3 P-36ESect-9.3 P-37ESect-9.3 P-38ESect-9.3 P-39ESect-9.3 P-40ESect-9.3 P-41ESect-9.3 P-42ESect-9.3 P-43ESect-9.3 P-44ESect-9.3 P-45ESect-9.3 P-46ESect-9.3 P-47ESect-9.3 P-48ESect-9.3 P-49ESect-9.3 P-50ESect-9.3 P-51ESect-9.3 P-52ESect-9.3 P-54ESect-9.4 P-1ESect-9.4 P-2ESect-9.4 P-5ESect-9.4 P-6ESect-9.4 P-7ESect-9.4 P-8ESect-9.4 P-9ESect-9.4 P-10ESect-9.4 P-11ESect-9.4 P-12ESect-9.4 P-13ESect-9.4 P-14ESect-9.4 P-16ESect-9.4 P-17ESect-9.4 P-18ESect-9.4 P-21ESect-9.4 P-22ESect-9.4 P-23ESect-9.4 P-24ESect-9.4 P-25ESect-9.5 P-1ESect-9.5 P-2ESect-9.5 P-3ESect-9.5 P-4ESect-9.5 P-5ESect-9.5 P-6ESect-9.5 P-7ESect-9.5 P-8ESect-9.5 P-9ESect-9.5 P-10ESect-9.5 P-11ESect-9.5 P-12ESect-9.5 P-13ESect-9.5 P-14ESect-9.5 P-15ESect-9.5 P-16ESect-9.5 P-17ESect-9.5 P-18ESect-9.5 P-19ESect-9.5 P-20ESect-9.5 P-21ESect-9.5 P-22ESect-9.5 P-23ESect-9.5 P-24ESect-9.5 P-25ESect-9.5 P-26ESect-9.5 P-27ESect-9.5 P-28ESect-9.5 P-29ESect-9.5 P-30ESect-9.5 P-31ESect-9.5 P-32ESect-9.5 P-33ESect-9.5 P-34ESect-9.5 P-35ESect-9.5 P-36ESect-9.5 P-37ESect-9.5 P-38ESect-9.6 P-1ESect-9.6 P-2ESect-9.6 P-3ESect-9.6 P-4ESect-9.6 P-5ESect-9.6 P-6ESect-9.6 P-7ESect-9.6 P-8ESect-9.6 P-10ESect-9.6 P-11ECh-9 P-1RCCCh-9 P-2RCCCh-9 P-3RCCCh-9 P-4RCCCh-9 P-5RCCCh-9 P-6RCCCh-9 P-7RCCCh-9 P-8RCCCh-9 P-9RCCCh-9 P-1RQCh-9 P-2RQCh-9 P-3RQCh-9 P-4RQCh-9 P-5RQCh-9 P-6RQCh-9 P-7RQCh-9 P-1RECh-9 P-2RECh-9 P-3RECh-9 P-4RECh-9 P-5RECh-9 P-6RECh-9 P-7RECh-9 P-8RECh-9 P-9RECh-9 P-10RECh-9 P-11RECh-9 P-12RECh-9 P-13RECh-9 P-14RECh-9 P-15RECh-9 P-16RECh-9 P-17RECh-9 P-18RECh-9 P-19RECh-9 P-20RECh-9 P-21RECh-9 P-22RECh-9 P-23RECh-9 P-24RECh-9 P-1PCh-9 P-2PCh-9 P-3PCh-9 P-4PCh-9 P-5PCh-9 P-6PCh-9 P-7PCh-9 P-8PCh-9 P-9PCh-9 P-10PCh-9 P-11PCh-9 P-12PCh-9 P-13PCh-9 P-14PCh-9 P-15P

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