Question

explore: what factors regulate population growth? the number of individuals in a population (called n) is calculated by knowing the gains and losses to the population. births (b) and immigration (i) increase the number of individuals in a population, while deaths (d) and emigration (e) decrease the number of individuals in a population. scientists determine the number of individuals in a population by counting them directly or by using sampling techniques. the rate of these events, e.g., number of births per unit time, is important. these rates are influenced by the resources available and the biology of the species. the biotic potential is a measure of a species capacity to increase and varies among species. some populations grow very rapidly and some very slowly. 1. using the terms b, d, i and e, develop an equation to describe how d, b, e, and i determine population growth. 2. now construct equations to express the following: (a) a population in equilibrium: (b) a declining population: (c) an increasing population: 3. a population started with 100 individuals. over a year, population data were collected. calculate birth rates, death rates, and net - migration rate, and use your equation to calculate the rate of population change for the data below (as percentages): (a) births = 14: birth rate = (b) net migration = +2: net migration rate = (c) deaths = 20: death rate = (d) rate of population change = (e) state whether the population is increasing or declining:

Explanation:

Step1: Define population - change formula

The change in population size ($\Delta N$) is given by the formula $\Delta N=(B - D)+(I - E)$, where $B$ is the number of births, $D$ is the number of deaths, $I$ is the number of immigrants, and $E$ is the number of emigrants.

Step2: Population in equilibrium

A population in equilibrium has $\Delta N = 0$. So, the equation is $B - D+I - E=0$ or $B + I=D + E$.

Step3: Declining population

A declining population has $\Delta N<0$. So, the equation is $B - D+I - E<0$ or $B + I

Step4: Increasing population

An increasing population has $\Delta N>0$. So, the equation is $B - D+I - E>0$ or $B + I>D + E$.

Step5: Calculate birth - rate

The birth - rate ($BR$) is calculated as $BR=\frac{B}{N}\times100\%$, where $N$ is the initial population. Given $B = 14$ and $N = 100$, $BR=\frac{14}{100}\times100\% = 14\%$.

Step6: Calculate death - rate

The death - rate ($DR$) is calculated as $DR=\frac{D}{N}\times100\%$. Given $D = 20$ and $N = 100$, $DR=\frac{20}{100}\times100\%=20\%$.

Step7: Calculate net - migration rate

The net - migration rate ($NMR$) is calculated as $NMR=\frac{I - E}{N}\times100\%$. Given $I - E = 2$ and $N = 100$, $NMR=\frac{2}{100}\times100\% = 2\%$.

Step8: Calculate rate of population change

The rate of population change ($RPC$) is $RPC=(BR - DR)+NMR$. Substituting the values: $RPC=(14 - 20)+2=-4\%$.

Step9: Determine population trend

Since $RPC=-4\%<0$, the population is declining.

Answer:

1. Equation for population growth: $\Delta N=(B - D)+(I - E)$
2. (a) Population in equilibrium: $B + I=D + E$

(b) Declining population: $B + I(c) Increasing population: $B + I>D + E$

1. (a) Birth rate: $14\%$

(b) Net migration rate: $2\%$
(c) Death rate: $20\%$
(d) Rate of population change: $-4\%$
(e) The population is declining.