2.6 Modelling skillsIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 2.6 Modelling skills

1. A rooftop water tank holds at most 400 litres. A pump starts filling the tank at $t=0$ minutes, and the volume of water $V$ litres in the tank is modelled by $V(t)=40+25t$.
   Find $V(20)$ and comment on the reasonableness of the model at $t=20$.2 marks
2. A scientist measures the mass $M$ grams of a radioactive sample $t$ days after the start: 80 g at $t=0$, 40 g at $t=6$ and 20 g at $t=12$. She wants to fit a model to these data.
   Use the model $M(t)=80a^t$, with $a$ from part (b), to predict the mass of the sample after 20 days.2 marks
3. A Ferris wheel has its lowest point 2 m above the ground and its highest point 52 m above the ground, and it completes one revolution every 20 minutes. A passenger is level with the axle, and rising, at $t=0$ minutes. The passenger's height $h$ metres above the ground is modelled by $h(t)=a\sin(bt^\circ)+d$, where $a,b>0$.
   Find the values of $a$, $b$ and $d$.3 marks