2.9 Further modelling functionsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.9 Further modelling functions

1. 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
2. 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
3. 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