For a lady bug population at the end of summer,the food supply decreases to where only 2000 lady bugs can be supported per acre.If there are 1000 lady bugs in a one-acre field,the per capita rate of increase is 25%,and no immigration or emigration occur,how many individuals will be added in the next generation? Interpret whether G = rN(K - N)/K or G = rN is appropriate.

Question

Quizplus · Accepted Answer

Applying the formula G = rN(K - N)/K assumes the population is growing in a logistic manner, which is not the case when there is a fixed carrying capacity (K) of 2000 ladybugs per acre. Therefore, we should use the simpler formula G = rN.

Given that the per capita rate of increase is 25%, we can calculate the net reproductive rate (r) as:

r = 0.25 + 1 = 1.25

This means that each ladybug will produce, on average, 1.25 offspring in the next generation. Since there are 1000 ladybugs in the current population, the expected number of new individuals (G) in the next generation is:

G = rN = 1.25 x 1000 = 1250

Therefore, the answer is B) 125.

For a Lady Bug Population at the End of Summer,the