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

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Further Modelling with Functions
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What type of function uses different formulas over different intervals?

Piecewise function

A taxi charges £3 for the first mile and £2 per extra mile. What is the cost for 4 miles?

£9

Which formula models exponential growth where P0P_0 is initial value and rr is growth rate?

P(t)=P0ertP(t) = P_0 \cdot e^{rt}

A population of 20,000 grows at 5% yearly. What is it after 10 years (using e0.51.6487e^{0.5} \approx 1.6487)?

32,974

Which scenarios are best modelled using quadratic functions?

Acceleration & projectile motion

A ball's height is h(t)=5+10t4.9t2h(t) = 5 + 10t - 4.9t^2. When does it hit the ground (approx)?

2.46 seconds

Logarithmic functions model situations where growth does what over time?

Slows down

What is the formula for pH in terms of hydrogen ion concentration [H+][H^+]?

pH=log[H+]pH = -\log[H^+]

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)?

0.1x2+30x500-0.1x^2 + 30x - 500

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

150 units

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