Further Modelling with Functions (Edexcel A-Level Mathematics): Quizzes

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Further Modelling with Functions
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When are piecewise functions most useful for modelling?

Different functions over different intervals

Using C(x)=3C(x) = 3 if 0<x10 < x \leq 1 and C(x)=3+2(x1)C(x) = 3 + 2(x-1) if x>1x > 1, find C(3)C(3) in £.

£7£7

In exponential growth P(t)=P0ertP(t) = P_0 \cdot e^{rt}, what does rr represent?

Growth rate

A population of 20,00020,000 grows at 55% per year. What is it after 1010 years (approx.)?

32,97432,974

Which scenario is quadratic modelling ideal for?

Projectile motion

What is the height function for projectile motion with initial height h0h_0 and velocity v0v_0?

h(t)=h0+v0t12gt2h(t) = h_0 + v_0t - \frac{1}{2}gt^2

A ball thrown from 55m with 1010 m/s velocity hits the ground after how many seconds (approx.)?

2.462.46 seconds

What type of situations do logarithmic functions model?

Growth that slows down over time

If C(x)=500+20xC(x) = 500 + 20x and R(x)=50x0.1x2R(x) = 50x - 0.1x^2, what is the profit function P(x)P(x)?

P(x)=0.1x2+30x500P(x) = -0.1x^2 + 30x - 500

To maximise profit from P(x)=0.1x2+30x500P(x) = -0.1x^2 + 30x - 500, how many units should be produced?

150150 units

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