Suppose That We Model Populations (In Millions) of Predators and Preys

question 88

Multiple Choice

Suppose that we model populations (in millions) of predators and preys with the system of differential equations: $\begin{array} { l } \frac { d x } { d t } = 2 x - 1.2 x y \\\frac { d y } { d t } = - y + 0.9 x y\end{array}$ Find the expression for $\frac { d y } { d x }$ .

• A) \(\frac { 2 x - 1.2 x y } { - y + 0.9 x y }\)
• B) \(\frac { - 2 x + 1.2 x y } { - y + 0.9 x y }\)
• C) \(\frac { 2 x - 1.2 x y } { y - 0.9 x y }\)
• D) \(\frac { 2 x - 1.2 x y } { - y - 0.9 x y }\)
• E) \(\frac { y - 0.9 x y } { 2 x - 1.2 x y }\)
• F) \(\frac { - y + 0.9 x y } { 2 x - 1.2 x y }\)
• G) \(\frac { - y + 0.9 x y } { - 2 x + 1.2 x y }\)
• H) \(\frac { - y + 0.9 x y } { - 2 x - 1.2 x y }\)

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Definitions:

Demand Decrease

A situation where there is a reduction in the quantity of a good or service that consumers are willing and able to purchase at any given price.

Equilibrium

A condition or state in which economic forces are balanced, such as the point where supply equals demand.

Market Clear

A situation in which the market reaches a state where quantity supplied equals quantity demanded, leaving no surplus or shortage.

Surplus

An excess of income or assets over expenditure or liabilities in a given period, typically a fiscal year, leading to available resources beyond what is required.