Population dynamics : Suppose a population of fish contains a females that are 1 year old, b females between 2 and 4 years old, and c females more than 4 years old. During the summer each one-year-old females produces 15 offspring, each female between 2 and 4 years prodoucs 35 off-spring and each female more than 4 years old produces 20 offspring. if a=[a,b,c] and p=[15,35,20], what is the meaing of the dot product a.p?

The dot product of a and p means the multiplication of the two sets giving the total fishes. The group a represents the number of female fishes, for example a=[6,7,8] . p=[15,35,20]

a represents the number of fishes in the age group 6 is the number 1 year old female fishes, 7 is the number 2 to 4 year old fishes and 8 is the number of 4 year old fishes.

p represents the number of off spring a single fish produces. 1 year old female fish produces 15 off springs in the summer, 2 to 4 year old female fish produces 35 off springs and above 4 year old fish produces 20 off springs.

If we multiply the two sets and add the product we will get the total number of fishes in the summer.