2.9 Further modelling functionsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

Formula for exponential decay with half-life T?
What is a half-life?
The natural logarithmic model?
What is a in f(x)=a+b\ln x?
Asymptote of f(x)=a+b\ln x?
The sinusoidal model?
Amplitude, period, phase shift, principal axis of a\sin(b(x-c))+d?
What angle unit is assumed for HL trigonometric models?
The logistic model?
What is the carrying capacity in a logistic model?
The starting value of a logistic model?
How do you make a piecewise function continuous?

Exam questions on 2.9 Further modelling functions

A radioactive isotope decays so that its mass $m$ mg after $t$ hours is modelled by $m=80\left(\frac12\right)^{t/6}$ , for $t\ge0$ .
Find the time at which the mass of the isotope is 5 mg.2 marks
The height $H$ metres of a tree $x$ years after planting ( $x\ge1$ ) is modelled by $H=a+b\ln x$ , where $a$ and $b$ are constants. When $x=1$ , $H=2$ , and when $x=e^{2}$ , $H=5$ .
Use your GDC to find the age at which the tree is 7 m high.2 marks
The depth $d$ metres of water at a harbour entrance, $t$ hours after midnight, is modelled by $d(t)=2.5\sin\left(\frac{\pi}{6}(t-1)\right)+6$ , for $0\le t\le24$ , where the angle is in radians.
Write down (i) the minimum depth, (ii) the period of the model, (iii) the phase shift.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).