Differential Equations (Edexcel A-Level Mathematics): Quizzes

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Modelling with Differential Equations
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Which field is NOT mentioned as using differential equation models?

Astronomy

What is the first step in modelling with differential equations?

Identify the variables

For exponential growth proportional to population size, which equation is correct?

dPdt=kP\frac{dP}{dt} = kP

In P(t)=P0ektP(t) = P_0 e^{kt}, what happens to the population if k>0k > 0?

Population grows exponentially

What type of differential equation is dPdt=kP\frac{dP}{dt} = kP?

Separable

Newton's Law of Cooling states the rate of change is proportional to what?

Temperature difference

In Newton's Law of Cooling, what does T(t)T(t) approach as time increases?

Room temperature TrT_r

What type of equation is d2xdt2+kmx=0\frac{d^2x}{dt^2} + \frac{k}{m}x = 0 for harmonic motion?

Second-order linear

In harmonic motion, what is the angular frequency ω\omega equal to?

km\sqrt{\frac{k}{m}}

What does P0P_0 represent in the solution P(t)=P0ektP(t) = P_0 e^{kt}?

Initial population at t=0t = 0

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