A population has the following characteristics. (a) A total of 25% of the population survives the first year. Of that 25%, 75% survives the second year. The maximum life span is 3 years. (b) The average number of offspring for each member of the population is 3 the first year, 6 the second year, and 3 the third year. The population now consists of 176 members in each of the three age classes. How many members will there be in each age class in 1 year

Starting with the members of age class 0. They produce 3 offsprings each during the first year, leading to 3×176 = 528 new members of age class 0 as at the end of the first year.

Then, of the 176 members of age class 0, only 25% make it to the next age class after a year, that is, only 44 of them.

So, from this group, after a year, age class 0 has 528 members, and age class 1 has 44 members.

Age class 1 group now. Population at the start = 176

They produce 6 offsprings each during that 1 year, that is, 6×176 = 1,056 new members of age class 0 at the end of that year.

Then, the survival rate for those in their second year of living is 75%, hence, 132 of them make it to the next age class.

So, from this group, after a year, age class 0 has 1056 members, and age class 2 has 132 members.

Age class 2 group now. Population at the start = 176

They produce 3 offsprings each during that 1 year, that is, 3×176 = 528 new members of age class 0 at the end of that year.

Then, the survival rate for those in their third year of living is 0%, hence, none of them make it to the next age class.

So, from this group, after a year, age class 0 has 528 members, and they all die off at the end of that 1 year.

So, we now calculate the number of members of each age class now at the end of that 1 year.

Age class 0 = 528 + 1056 + 528 = 2112 members

Age class 1 = 44 members

Age class 2 = 132 members.

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