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

question 110

Multiple Choice

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 $k y ^ { 1.03 }$ . If 3 such rabbits breed initially and the warren has 28 rabbits after 5 months, then when is doomsday?

• A) \(127.15\) months
• B) \(97.15\) months
• C) \(77.15\) months
• D) \(147.15\) months
• E) \(167.15\) months

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Definitions:

Menisci

Curved fibrocartilaginous structures in the knee joint that serve to distribute weight and reduce friction during movement.

Cartilage

A flexible connective tissue found in various forms in the body, including joints, ear structure, and the nose.

Synovial Joints

Synovial joints are the most movable type of joint in the body, characterized by a cavity filled with synovial fluid, which allows for smooth movement between the bones.

Discoidal

Pertaining to a disc-like shape; often used to describe the shape of certain blood cells, notably red blood cells, or other structures.