Mathematical Studies: Mathematical Models Topical Past Paper Questions

Jean-Pierre jumps out of an airplane that is flying at constant altitude. Before opening his parachute, he goes through a period of freefall. Jean-Pierre's vertical speed during the time of freefall, S, in m s^{-1}, is modelled by the following function. $$ S(t)=K-60\left(1.2^{-t…

[Maximum mark: 16] The graph of the quadratic function $ f(x)=\frac{1}{2}(x-2)(x+8) $ intersects the y-axis at $ (0, c) $. (a) Find the value of $ c $. The vertex of the function is $ (-3, -12.5) $. (b) Write down the equation for the axis of symmetry of the graph. The equation $…

The amount of yeast, g grams, in a sugar solution can be modelled by the function, $$ g(t)=10-k(c^{-l})\mathrm{~f o r~}t\geq0 $$ where $t$ is the time in minutes. The graph of $g(t)$ is shown. The initial amount of yeast in this solution is 2 grams. (a) Find the value of k. [2] T…