Exercise · ZW-DIFFERENTIAL-EQUATION-008 · ★★☆ Intermediate
If the rate of change of a population \(P\) with respect to time is proportional to \(P\), the model is:
Choose one option.
Show answer
- A. \(\dfrac{dP}{dt}=kP\)
Explanation
«Rate of change» is the derivative \(dP/dt\), and «proportional to \(P\)» means \(kP\).
Review the concept: Differential equation
A differential equation is an equation \(F=0\) whose unknown is a function \(y\) and which relates it to one or more of its derivatives.
\[F\left(x,\,y,\,y',\,\dots,\,y^{(n)}\right)=0\]
More practice problems: differential equation
- ZW-DIFFERENTIAL-EQUATION-001 Which of the following is a differential equation?
- ZW-DIFFERENTIAL-EQUATION-002 In (dy)/(dt)=-0.5 y, which is the independent variable?
- ZW-DIFFERENTIAL-EQUATION-003 Differentiating y=Ce^3x and eliminating the constant C gives the equation:
- ZW-DIFFERENTIAL-EQUATION-004 Which of the following is NOT a differential equation?
- ZW-DIFFERENTIAL-EQUATION-005 Differentiating y=x^2+C and eliminating C gives:
- ZW-DIFFERENTIAL-EQUATION-006 Which of the following differential equations involves partial derivatives?
- ZW-DIFFERENTIAL-EQUATION-007 Which function satisfies the equation y''+y=0?
- ZW-DIFFERENTIAL-EQUATION-009 Solving y'=2y means finding:
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