Assume That $a > 0$ $b > 0$ the Autonomous Differential Equation

question 13

Multiple Choice

Assume that $a > 0$ , $b > 0$ . The autonomous differential equation $\frac { d P } { d t } = P ( a + b P )$ has a solution that is

• A) increasing everywhere
• B) decreasing everywhere
• C) increasing if \(- a / b < P < 0\)
• D) decreasing if \(- a / b < P < 0\)
• E) decreasing if \(P < - a / b\)

---

Definitions:

Opportunity Cost

The charge of overlooking the next most beneficial alternative while making a choice.

Consumer Goods

Goods that are produced and purchased for personal use, satisfying direct consumer wants and needs.

Opportunity Cost

Waiving the opportunity for improvement from multiple choices by deciding on one.

Linear Production

A type of production process where output increases at a constant rate as more inputs are added.