Q: A population of 100 rabbits has a geometric growth rate ($$\lambda) of 1.2. $$What will the population size be after 3 time intervals, assuming discrete generations?

$$N_3 = 100$$ \times $$1.2^3 = 172.8$

Q: A population of birds has $$N_0 = 200$ and r = 0.05$. What will the population size be after 10 years, assuming exponential growth?

$$N_{10} = 200 \times e$$^{0.05 \times 10}$$ \approx 200 \times e$$^{0.5}$$ \approx 329$$

Question 1

Which of the following best describes a closed population in the context of population dynamics?

Accepted Answer

A population with no immigration or emigration.

Question 2

In the exponential growth model, which equation correctly predicts the population size at time $$t$$ for a continuously reproducing population?

Accepted Answer

$$N_t = N_0$ e$$^{rt}$$

Question 3

A population of 100 rabbits has a geometric growth rate ($$\lambda) of 1.2. $$What will the population size be after 3 time intervals, assuming discrete generations?

Accepted Answer

$$N_3 = 100$$ 	imes $$1.2^3 = 172.8$

Question 4

Which of the following is the correct relationship between the exponential growth rate $$r$$ and the geometric growth rate $$\lambda$$?

Accepted Answer

$$\lambda = e^r$$

Question 5

If a population has an instantaneous birth rate $$b = 0.4$$ and an instantaneous death rate $$d = 0.1$$, what is the intrinsic rate of increase $$r$$?

Accepted Answer

$$r = b - d = 0.3$$

Question 6

Which scenario would most likely result in a population decreasing in size over time?

Accepted Answer

$$\lambda \u003c 1 or$$ $$r \u003c 0$$

Question 7

A population of salmon breeds once per year and then dies. Which mathematical model best describes the growth of this population?

Accepted Answer

Geometric growth model

Question 8

Given the exponential growth equation $$dN/dt = rN$$, which of the following is an assumption of this model?

Accepted Answer

Resources are unlimited and $$r is $$constant.

Question 9

If a population of 50 insects grows continuously with $$r = 0.2$$, how long will it take for the population to double? (Use $$t_d = \frac{\ln 2}{r})$$

Accepted Answer

$$t_d = \frac{\ln 2}{0.2} \approx 3.47$$

Question 10

Which of the following best explains why the reindeer population on St. Matthew’s Island grew exponentially after introduction?

Accepted Answer

There were abundant resources and few predators, allowing for continuous reproduction.

Question 11

Which equation would you use to calculate the population size after $$t$$ time intervals for a population with non-overlapping generations?

Accepted Answer

$$N_t = N_0$ \lambda^t$$

Question 12

A population of birds has $$N_0 = 200$ and r = 0.05$. What will the population size be after 10 years, assuming exponential growth?

Accepted Answer

$$N_{10} = 200 	imes e$$^{0.05 	imes 10}$$ \approx 200 	imes e$$^{0.5}$$ \approx 329$$

Question 13

Which of the following is NOT an assumption of the exponential growth model?

Accepted Answer

Population has age or size structure.

Question 14

If $$\lambda = 1.0$$ for a population, what does this indicate about the population size over time?

Accepted Answer

The population size remains constant.

Question 15

Which of the following best describes the difference between geometric and exponential growth?

Accepted Answer

Geometric growth occurs in populations with discrete generations, while exponential growth occurs in populations with overlapping generations.

Question 16

A population of tropical insects reproduces continuously. Which parameter would you use to describe its growth rate?

Accepted Answer

Intrinsic rate of increase ($$r)$$

Question 17

If a population’s per capita birth rate is 0.6 and per capita death rate is 0.6, what is the expected behavior of the population size?

Accepted Answer

The population size will remain constant.

Question 18

Which of the following real-world examples best fits the geometric growth model?

Accepted Answer

Migratory birds that breed once per year.

Question 19

Which formula would you use to calculate the geometric growth rate ($$\lambda) $$from population sizes at two consecutive time intervals?

Accepted Answer

$$\lambda = \frac{N_{t+1}}{N_t}$$

Question 20

A population of 500 marine invertebrates is open, with frequent immigration and emigration. Which equation best describes the change in population size?

Accepted Answer

$$\Delta N = (B + I) - (D + E)$$

5.1 Population Dynamics: Exponential and Geometric Growth

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