Chapter 36, Problem 1CC

Use this graph of the idealized exponential and logistic growth curves to complete the following.

a. Label the axes and curves on the graph.

b. Give the formula that describes the blue curve.

c. What does the dotted line represent?

d. For each curve, indicate and explain where population growth is the most rapid.

e. Which of these curves best represents global human population growth?

Summary Introduction

To label: The axis and the curves of the graph.

Introduction: Exponential growth curve is the J-shaped curve that is ever increasing in nature. The logistic growth curve is an S shaped curve in which the growth of the population ceases after a certain point which can be represented as the carrying capacity of the population.

Answer to Problem 1CC

Correct answer:

X-axis is time, Y-axis is population size. Blue/thick curve is the exponential growth and red/thin curve is logistic curve

Explanation of Solution

Graphical representation: Fig: 1 shows the graph depicting the logistic and exponential growth curve.

Fig. 1: The graph depicting the logistic and exponential growth curve.

The X-axis of the graph represents the time taken for growth and the Y-axis of the graph represents the size of the population. The blue/thick curve is the exponential growth curve and red/thin curve is logistic growth curve. Hence the correct answer is X-axis is time, Y-axis is population size. Blue/thick curve is the exponential growth and red/thin curve is logistic curve

Summary Introduction

To give: The formula that describes the blue curve.

Answer to Problem 1CC

Correct answer:

$\text{G=rN}$

Explanation of Solution

Refer to Fig.1; the blue curve can be described by the formula $\text{G=rN}$, where G is the growth, r is the rate of growth and N is the population size. Hence the correct answer is $\text{G=rN}$

Summary Introduction

To determine: What does the dotted line represents.

Answer to Problem 1CC

Correct answer:

Carrying capacity of the environment (K)

Explanation of Solution

Refer to Fig.1; the dotted line represented on the graph is the carrying capacity of the environment. Hence the correct answer is carrying capacity of the environment (K)

Summary Introduction

To determine: What does each curve represents.

Answer to Problem 1CC

Correct answer:

Population of logistic curve is most rapid at half of the carrying capacity. Population of exponential growth is most rapid throughout the curve as it is continuously increasing.

Explanation of Solution

Refer to Fig.1; the population growth is most rapid when population attains half of the carrying capacity in logistic curve and the population growth is continuously increasing in the exponential growth curve. Hence the correct answer half of the carrying capacity in logistic curve and continuous growth in exponential growth.

Summary Introduction

To determine: The curve which represents the global human population.

Answer to Problem 1CC

Correct answer:

Exponential growth curve

Explanation of Solution

Refer to Fig.1; it is the J shaped curve that is continuously increasing is the exponential growth curve. The worldwide population can be represented by this curve as the population is ever increasing. Hence the correct answer is exponential growth curve.