Question

The population of mosquitoes in a swamp is estimated over the course of twenty weeks, as shown in the table.

Time(weeks) Population
0 100
5 1,000
10 10,000
15 100,000
20 1,000,000

Which of the following best describes the relationship between time and the estimated population of mosquitoes during the twenty weeks?

A Increasing linear
B Decreasing linear
C Exponential growth
D Exponential decay

Answer 1

The population of mosquitoes in a swamp increases exponentially over twenty weeks, with each week representing a tenfold increase in numbers.

Therefore, the correct answer is: option C) Exponential growth

Step-by-step explanation:

Exponential growth is a process that increases quantity over time at an ever-increasing rate. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.

In this case, the relationship between time and the estimated mosquito population in the swamp over twenty weeks is best described as exponential growth. As time increases, the population grows by a consistent rate to the power of the number of time intervals.

Each time interval (measured in weeks) corresponds to a tenfold increase in the mosquito population, which is a characteristic of exponential growth patterns.

The exponential growth model describes a population with unlimited resources, which keeps growing bigger and faster over time.