Question

1. a herd of zebras has 9 males and 62 females. during a one - year period, 22 foals that are born survive and 25 adults die. six females join the herd. three males and 11 females leave the herd. has the herd reached its carrying capacity for this ecosystem? how do you know?

○a. the herd has reached its carrying capacity because the growth rate is negative.
○b. the herd has reached its carrying capacity because the growth rate is positive.
○c. the herd has not reached its carrying capacity because the growth rate is negative.
○d. the herd has not reached its carrying capacity because the growth rate is positive.

1. draw a graph of logistic growth. label the point at which the resources for the population cannot support exponential growth.

Explanation:

Step1: Calculate initial population

Initial number of zebras \(=9 + 62=71\)

Step2: Calculate population change

Births (foals survive) \(=22\), Deaths \(=25\), Immigration (females join) \(=6\), Emigration (males and females leave) \(=3 + 11 = 14\)
Population change formula: \(\text{Population change}=\text{Births}-\text{Deaths}+\text{Immigration}-\text{Emigration}\)
Substitute values: \(22-25 + 6-14=-11\)
Growth rate is negative (\(-11\))

When a population reaches carrying capacity, growth rate approaches zero. Since growth rate is negative (\(-11\)), the herd has not reached carrying capacity.

Answer:

C. The herd has not reached its carrying capacity because the growth rate is negative.