Question

calculating the growth rate
the growth rate of a population can be measured with an equation that takes into account the four factors that affect population size:
r=(b + i)-(d + e)
in this equation, (r =) population growth rate, (b =) birth rate, (i =) immigration rate, (d =) death rate, and (e =) emigration rate. we can apply the four - factors to our locker ecosystem example. a small population of fruit flies immigrated into the locker in search of food. the population increased due to the birth of a new group of fruit flies. those flies that did not die when you swatted them in surprise emigrated from the locker when you threw the apple away.
as part of a long - term elephant study, biologists counted individuals in a population of elephants each spring. in one year, there were 18 males and 34 females. over the following year, each female gave birth, from which 28 offspring survived. predators killed 9 elephants. a construction project cleared 50 acres of nearby forested land, causing 5 males and 19 females to immigrate into the study area. competition for females increased, resulting in the emigration of 10 males to a new territory in search of mates.
solve find the growth rate of this population. show your work.
r=(b + i)-(d + e)

Explanation:

Step1: Calculate initial population size

Initial number of males = 18, initial number of females = 34. Initial population size $N_0=18 + 34=52$.

Step2: Calculate birth rate ($b$)

Number of surviving offspring = 28, initial number of females = 34. $b=\frac{28}{34}\approx0.824$.

Step3: Calculate immigration rate ($i$)

5 males and 19 females immigrated. $i=\frac{5 + 19}{52}=\frac{24}{52}\approx0.462$.

Step4: Calculate death rate ($d$)

9 elephants were killed by predators. $d=\frac{9}{52}\approx0.173$.

Step5: Calculate emigration rate ($e$)

10 males emigrated. $e=\frac{10}{52}\approx0.192$.

Step6: Calculate population growth rate ($r$)

Using the formula $r=(b + i)-(d + e)$.
$r=(0.824+ 0.462)-(0.173 + 0.192)$
$r = 1.286-0.365$
$r=0.921$.

Answer:

The population growth rate is approximately $0.921$ elephants per year.