Suppose the weight of an animal and its pulse satisfy an all

Suppose the weight of an animal and its pulse satisfy an allometric model, given by P = kw^a, where P is the pulse and w is weight. A human weighs 68 kg and has a pulse of 65 beats/min and a rabbit weighs 1.35kg and has a pulse of 170 beats/min. a. Find the constants k and a in the allometric model. Round answers to 3 decimal places. b. Use the model to find the weight of an animal that has a pulse of 134 beats/min.

Solution

a) 65 = k*68^a and 170 = k*1.35^a

Dividing both ======> 2.62 = 50.37^a ======> ln 2.62 = a*ln50.37

a = 0.246

and k = 23.05

b) 134 = 23.05*w^0.246

w^0.246 = 5.813

w = 1280.32 kg