Allometric growth in biology refers to relationships between sizes of parts of an organism (skull length and body length, for instance). If L1(t) and L2(t) are the sizes of two organs in an organism of age t, then L1 and L2satisfy an allometric law if their specific growth rates are proportional:
1/L1 dL1/dt = k 1/L2 dL2/dt
where k is a constant.
(a) Use the allometric law to write a differential equation relating L1 and L2 solve it to express L1 as a function of L2.
(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.