Chapter 51, Problem 1TYK

CAUTION What is the defining feature of exponential growth?

a. The population is growing.

b. The per capita growth rate is constant.

c. The per capita growth rate increases rapidly over time.

d. The per capita growth rate is very high.

Summary Introduction

Introduction:

The type of growth where the population grows rapidly without any decline is called exponential growth. It is also the rate of change per unit time. The population size in the exponential growth does not limit the growth rate.

Answer to Problem 1TYK

Correct answer:

The defining feature would be that the per capita growth rate is constant. The per capita growth rate does not change during the exponential growth.

Explanation of Solution

Justification for the correct statement:

Option (b) is given that the per capita rate remains constant. During the exponential growth, the per capita growth rate is constant, unlike the logistic growth. It does not depend on the population size. Per capita growth rate if is higher, the population size increases gradually.

The per capita growth rate is given as the function of “N” (population size) and “t” (time interval) and is represented as $r=\frac{\text{d}N}{\text{d}t}$, where “r” is per capita growth rate. The value of “r” is high if the increase in the population within a short interval of time is high. Thus, the large value of “r” indicates the increased population size. Hence, option (b) is correct.

Justification for the incorrect statements:

Option (a) is given that the population is growing. In the exponential growth rate, the population grows rapidly; however, it is not a defining feature. So, it is incorrect.

Option (c) is given that the population experiences high rates of predation. The increase in the size does not depend on the exponential growth. Even if the per capita rate is high, but constant, the larger population still tends to become larger rapidly when compared to the small population as the initial number of population is high. So, it is incorrect.

Option (d) is given that the per capita growth rate is quite high. Per capita growth rate does not increase rapidly and the growth rate is not very high. The growth occurs gradually. So, it is incorrect.

Hence, the options (a), (c), and (d) are incorrect.

Conclusion

Thus, the constant per capita growth rate of the populations serves as the defining feature of the exponential growth rate.