The volume of gas, VVV liters, in a high-altitude research balloon is recorded as it rises through the atmosphere. The altitude is measured as hhh km above the launch site.
When the balloon is exactly 5 km above the launch site, the volume is measured as 30 liters.
When the balloon is exactly 10 km above the launch site, the volume is measured as 50 liters.
Given that the relationship between the volume and altitude is modelled by the equation
V2=p+qh2 V^2 = p + qh^2 V2=p+qh2where ppp and qqq are constants,
find the exact value of ppp and the exact value of qqq.
According to the model, the volume of the balloon reaches 80 liters at an altitude of exactly HHH km.
Making your method clear,
find the value of HHH, giving your answer to one decimal place.
(Solutions relying entirely on calculator technology are not acceptable.)
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
