Let $c$ Be a Positive Number $$\frac { d y } { d t } = k y ^ { 1 + c }$$

question 117

Short Answer

Let $c$ be a positive number. A differential equation of the form
$$\frac { d y } { d t } = k y ^ { 1 + c }$$
where $k$ is a positive constant is called a doomsday equation because the exponent in the expression $k y ^ { 1 + c }$ is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term $k y ^ { 1.05 }$ . If 4 such rabbits breed initially and the warren has 23 rabbits after 6 months, then when is doomsday?

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Definitions:

Bottom-Up Processing

Analysis that begins with the sensory receptors and works up to the brain’s integration of sensory information.

Subliminal Priming

The use of stimuli presented below the threshold of conscious perception to influence thoughts, feelings, or actions.

Conscious Awareness

The mental state of being fully present and aware of oneself and the surroundings.

Subliminal Sounds

Sounds that are played below the conscious level of hearing, purportedly influencing behavior or perception.