Table of contents

1. Introduction to Biology2h 42m
2. Chemistry3h 37m
3. Water1h 26m
4. Biomolecules2h 23m
5. Cell Components2h 26m
6. The Membrane2h 31m
7. Energy and Metabolism2h 0m
8. Respiration2h 40m
9. Photosynthesis2h 49m
10. Cell Signaling59m
11. Cell Division2h 47m
12. Meiosis2h 0m
13. Mendelian Genetics4h 44m
14. DNA Synthesis2h 27m
15. Gene Expression3h 6m
16. Regulation of Expression3h 31m
17. Viruses37m
- Viruses
  37m
18. Biotechnology2h 58m
19. Genomics17m
- Genomes
  17m
20. Development1h 5m
21. Evolution3h 1m
22. Evolution of Populations3h 53m
23. Speciation1h 37m
24. History of Life on Earth2h 6m
25. Phylogeny2h 31m
26. Prokaryotes4h 59m
27. Protists1h 12m
28. Plants1h 22m
29. Fungi36m
- Fungi
  19m
- Fungi Reproduction
  17m
30. Overview of Animals34m
- Overview of Animals
  34m
31. Invertebrates1h 2m
32. Vertebrates50m
33. Plant Anatomy1h 3m
34. Vascular Plant Transport1h 2m
- Water Potential
  1h 2m
35. Soil37m
- Soil and Nutrients
  20m
- Nitrogen Fixation
  16m
36. Plant Reproduction47m
- Flowers
  33m
- Seeds
  14m
37. Plant Sensation and Response1h 9m
38. Animal Form and Function1h 19m
39. Digestive System1h 10m
- Digestion
  1h 3m
- Blood Sugar Homeostasis
  7m
40. Circulatory System1h 49m
41. Immune System1h 12m
42. Osmoregulation and Excretion50m
- Osmoregulation and Excretion
  50m
43. Endocrine System1h 4m
- Endocrine System
  1h 4m
44. Animal Reproduction1h 2m
- Animal Reproduction
  1h 2m
45. Nervous System1h 55m
- Neurons and Action Potentials
  1h 8m
- Central and Peripheral Nervous System
  46m
46. Sensory Systems46m
- Sensory System
  46m
47. Muscle Systems23m
- Musculoskeletal System
  23m
48. Ecology3h 11m
49. Animal Behavior28m
- Animal Behavior
  28m
50. Population Ecology3h 41m
51. Community Ecology2h 46m
52. Ecosystems2h 36m
53. Conservation Biology24m
- Conservation Biology
  24m

50. Population Ecology

Logistic Population Growth

General Biology

50. Population Ecology

Logistic Population Growth

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Multiple Choice

A population of spotted hyenas in a South African National Park currently has 87 individuals. The carrying capacity for spotted hyenas in the park is estimated to be 125 hyenas & the intrinsic growth rate ( $r$ ) is 0.25 hyenas/year/hyena. What is the instantaneous rate of population growth of the spotted hyena population?

22 hyenas/year.

7 hyenas/year.

15 hyenas/year.

13 hyenas/year.

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Verified step by step guidance

Understand the concept of population growth: The instantaneous rate of population growth can be calculated using the logistic growth model, which considers the current population size, carrying capacity, and intrinsic growth rate.

Identify the formula for logistic growth: The formula to calculate the instantaneous rate of population growth is $ \frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right) $, where $ N $ is the current population size, $ r $ is the intrinsic growth rate, and $ K $ is the carrying capacity.

Substitute the given values into the formula: Use $ N = 87 $, $ r = 0.25 $, and $ K = 125 $ in the formula $ \frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right) $.

Calculate the term $ \left(1 - \frac{N}{K}\right) $: This represents the proportion of the carrying capacity that is still available for growth. Substitute $ N = 87 $ and $ K = 125 $ to find this value.

Multiply the intrinsic growth rate $ r $, the current population size $ N $, and the calculated proportion $ \left(1 - \frac{N}{K}\right) $ to find the instantaneous rate of population growth.