Please explain how to do all the parts to the question 2. You are studying some
ID: 91743 • Letter: P
Question
Please explain how to do all the parts to the question
2. You are studying some parthenogenic tarantulas with a population size of 300 individuals in a canyon where there is no possibility of migration. The canyon is huge and has an essentially unlimited supply of food and water for the tarantulas. During a one-month period, you record 40 births and 15 deaths. Assume that this population grows continuously.
(a) Estimate r and project the population size in 6, 12, and 18 months
(b) There is hard rain that floods the canyon and only 150 tarantulas survive. Project the population size in 6, 12, and 18 months.
Explanation / Answer
2) a) Initial population= 300
In one month, there are 40 births and 15 deaths. So, population grows by 25 in one month period.
X t = X o (1 + r t)
325 = 300 (1+ r 1)
0.923 = 1 + r
r = 0.077
Growth rate (r) = 7.7%
Population size at 6 months
= 300 (1 + 0.077 6)
= 300 (1+2.08)
= 300 (3.08)
= 924
Population growth at 12 months
= 300 (1+ 0.077 12)
= 300 (1+4.34)
= 300 (5.34)
= 1602
Population growth at 18 months
= 300 (1+ 0.077 18)
= 300 (1+ 9.05)
= 300 (10.05)
= 3150
b) If initial population is 150, the population size at the end of 6 months is
= 150 (1+ 0.07 6)
= 150 (1+ 2.08)
= 150(3.08)
= 462
Population size at 12 months
= 150 (1+ 0.07 12)
= 801
Population size at 18 months
= 150(1+ 0.07 18)
= 150(10.05)
= 1575