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.)
80 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.