Q1ITD Assuming that r聽= 1.0 and K聽= ... [FREE SOLUTION]

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Chapter 53: Q1ITD (page 1188)

Assuming that r= 1.0 and K= 1,500, calculate the population growth rate for four cases where population size (N) is greater than carrying capacity (K): N= 1,510, 1,600, 1,750, and 2,000 individuals. To do this, first write the equation for the population growth rate given in Table 53.2. Plug in the values for each of the four cases, starting with N= 1,510, and solve the equation for each
one. Which population size has the highest growth rate?

Short Answer

Expert verified

According to table 53.2, the population growth rate is calculated by using the formula-

\(rN\frac{{K - N}}{K}\)

Here, r-intrinsic rate of increase\( = 1.0\)

N-Population size=1510,1600,1750, and 2000

K-carrying capacity\( = 1500\)

By using formula-

For population size 1510, the population growth rate will be=\( - 10.06\)

For population size 1600, the population growth rate will be=\( - 106.06\)

For population size 1750, the population growth rate will be=\( - 291.66\)

For population size 2000, the population growth rate will be=\( - 666.66\)

The population growth rate is in the negative mode, so this indicates that the population is increasing with a negative growth rate. Thus, the highest growth rate will be of population size- 1510

Step by step solution

Step 1: Population Growth

Population growth is the increase in the number of individuals in a population of species. In humans, this is around 83 million annually at the global level.

The population growth rate can be positive or negative, which means the population can increase or decrease over time. It depends on the births and deaths of individuals.

Step 2: Carrying Capacity

Carrying capacity is the population size of a species below which population increases and above which it tends to decrease because resources start to diminish for above that size of the population. It is different for different species because the needs of these species are different.

Step 2: Population Growth rate

Formula for population growth rate is

\(rN\frac{{K - N}}{K}\)

Here, r-intrinsic rate of increase=1.0

N-Population size=1510,1600,1750, and 2000

K-carrying capacity=1500

So for a population size 1510, the population growth rate will be

\(1*1510\frac{{1500 - 1510}}{{1500}}\)

\(1510\frac{{ - 10}}{{1500}}\)

\(\frac{{ - 151}}{{15}}\)

\( - 10.06\)

So for a population size 1600, the population growth rate will be

\(1*1600\frac{{1500 - 1510}}{{1500}}\)

\(1600\frac{{ - 100}}{{1500}}\)

\(\frac{{ - 1600}}{{15}}\)

\( - 106.06\)

So for a population size 1750, the population growth rate will be

\(1*1750\frac{{1500 - 1510}}{{1500}}\)

\(1750\frac{{ - 250}}{{1500}}\)

\(\frac{{ - 4375}}{{15}}\)

\( - 291.66\)

So for population size 2000, the population growth rate will be

\(1*2000\frac{{1500 - 2000}}{{1500}}\)

\(2000\frac{{ - 500}}{{1500}}\)

\(\frac{{ - 10000}}{{15}}\)

\( - 666.66\)

A negative growth rate indicates that a negative growth rate increases the population, so the highest growth rate will be for population size 1510 that is -10.06.