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Chapter 53: Q7TYU (page 1188)

According to the logistic growth equation\(\frac{{dN}}{{dt}} = rN\frac{{(K - N)}}{K}\)

(A) the number of individuals added per unit time is greatest when Nis close to zero.

(B) the per capita population growth rate increases as Napproaches K.

(C) population growth is zero when Nequals K.

(D) the population grows exponentially when Kis small

Short Answer

Expert verified
  1. The statement 鈥渢he number of individuals added per unit time is greatest when Nis close to zero鈥� is false.
  2. The statement 鈥渢he per capita population growth rate increases as Napproaches K鈥� is false.
  3. The statement 鈥減opulation growth is zero when Nequals K鈥� is true.
  4. The statement 鈥渢he population grows exponentially when Kis small鈥� is false.

Step by step solution

01

Population ecology

The subdivision of ecology that focuses on species population and the associated change in them living in the same area including the environment, population size and distribution is called population ecology.

02

Explanation of option ‘(A)’

Logistic growth refers to a model that shows the growth rate of the population and its change as an exponential function.

Thus, the rate of the exponential increase of population slows down when N is close to zero.

Therefore, the given statement is false.

03

Explanation of option ‘(B)’

The growth rate in the logistic model shows the change in population rate over time based on the availability of resources like food space.

Thus, when N approaches K, the growth rate decreases.

Therefore, the given statement is false.

04

Explanation of option ‘(C)’

The birth rate, death rate, and migration are considered as three distinct elements affecting the population growth rate in the logistic model.

Thus, N (population density) is approaching K (carrying capacity); population growth does not grow exponentially and decreases with time until it becomes zero.

Therefore, the given statement is true.

05

Explanation of option ‘(D)’

The logistic growth curve indicates the exponential function of population growth with limited environmental resources.

Thus, when K (carrying capacity) is small, there will be no exponential growth of population.

Therefore, the given statement is false.

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Most popular questions from this chapter

  1. Find the intervals of increase or decrease.
  2. Find the local maximum and minimum values.
  3. Find the intervals of concavity and the inflection points.
  4. Use the information from parts (a)-(c) to sketch the graph. You may want to check your work with a graphing calculator or computer.

45. \(f\left( x \right) = {x^3} - 3{x^2} + 4\)

Mice that experience stress such as a food shortage will sometimes abandon their young. Explain how this behavior might have evolved in the context of reproductive trade-offs and life history.

The graph of the derivative \(f'\) of a continuous function \(f\) is shown

  1. On what intervals is f increasing? Decreasing?
  2. At what values of \(x\) does f have a local maximum? Local minimum?
  3. On what intervals is f concave upward? Concave downward?
  4. State the \(x\)-coordinate(s) of the point(s) of inflection.
  5. Assuming that \(f\left( 0 \right) = 0\), sketch the graph of f.

44.
  1. Find the intervals of increase or decrease.
  2. Find the local maximum and minimum values.
  3. Find the intervals of concavity and the inflection points.
  4. Use the information from parts (a)-(c) to sketch the graph. You may want to check your work with a graphing calculator or computer.

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