Business I / First-Order Differential Equations
Practice question · Match the pairs

Match each ODE to its economic model.

  • A˙=rA\dot{A} = rA
  • p˙=α(D−S)\dot{p} = \alpha(D - S)
  • k˙=sf(k)−δk\dot{k} = sf(k) - \delta k
  • A˙=−δA\dot{A} = -\delta A
  • Solow capital accumulation
  • Price adjustment toward equilibrium
  • Advertising awareness decay
  • Continuous compound interest
Hints
  1. Ask whether the rate is proportional, corrective, or constant.
  2. A rate proportional to the gap from a target is equilibrium-seeking.
Show the answer
  • A˙=rA\dot{A} = rA → Continuous compound interest
  • p˙=α(D−S)\dot{p} = \alpha(D - S) → Price adjustment toward equilibrium
  • k˙=sf(k)−δk\dot{k} = sf(k) - \delta k → Solow capital accumulation
  • A˙=−δA\dot{A} = -\delta A → Advertising awareness decay
Why

Each economic process has a differential equation: growth, equilibrium seeking, accumulation, and decay.

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