Question

A rabbit population rises and falls periodically over time. A researcher first started tracking the population of rabbits on January 1, 2010. It reached a minimum population of 250 on February 14, 2010 (day 45) and by May 14 (day 134), it reached a population of 575, which is the average for this population over time. Determine whether each statement is true or false. The sinusoidal axis is at y = 575.

Answer 1

The statement that the sinusoidal axis is at y = 575 is true because that value represents the average population of the rabbits over time, which meets the definition of the sinusoidal axis in the context of trigonometry or mathematical modeling.

Step-by-step explanation:

The question relates to the subject of Mathematics, specifically within the context of trigonometry or mathematical modeling of populations. Given the information about the population of rabbits, the statement 'The sinusoidal axis is at y = 575' is true. This is because the sinusoidal axis (also known as the midline of a sinusoidal function) is where the function oscillates above and below, and is equivalent to the average value of the function over one period. Since it was given that the average population over time is 575, this matches the definition of the sinusoidal axis. Therefore, the statement is accurate, and the sinusoidal axis is indeed at y = 575.

Answer 2

The statement that the sinusoidal axis is at y = 575 is true, as this represents the average rabbit population around which the population oscillates periodically.

Step-by-step explanation:

A rabbit population that rises and falls over time can be modeled by a sinusoidal function due to its periodic nature.

In this scenario, we are given specific dates when a minimum and an average population were recorded.

To analyze the given statements, we must understand the components of a sinusoidal function in the context of a rabbit population.

The claim that 'The sinusoidal axis is at y = 575' indicates that the average population level of rabbits serves as the horizontal axis around which the population oscillates.

This is typically true for sinusoidal functions representing periodic biological populations, where this axis is also known as the midline or equilibrium value.

True: The sinusoidal axis is at y = 575, indicating that this is the average population of rabbits, which is a common characteristic of such functions.

To fully determine the correctness of statements regarding the sinusoidal population model, we would need to consider additional specifics such as the amplitude, period, and phase shift, which are not provided by the given statements alone.

Hence, the statement that the sinusoidal axis is at y = 575 is true.