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

question 81

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 $k y ^ { 103 }$ . If 3 such rabbits breed initially and the warren has 28 rabbits after 5 months, then when is doomsday?

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Definitions:

Real Wages

Wages adjusted for inflation, reflecting the actual purchasing power of income earned from work.

Output per Worker

A measure of productivity calculated by dividing total output of goods or services by the number of workers involved in the production.

Productivity of Labor

The measurement of the output produced by employees per unit of input, such as per hour of work.

Diminishing Returns

A principle which states that as more units of a variable input (like labor) are added to fixed inputs (like capital), the additional output from each new unit of input will eventually decrease.