I have this maths problem for school that I cannot solve.
$a(x) = Ne^{kx}$ This exponential function can be calculated by looking at the maximum height of each bounce. $$\begin{array}{|c|c|} \hline & \rm First\: Bounce & \rm Second\: Bounce & \rm Third\: bounce\\\hline \rm Max\: Height & -0.277 & -0.350 & -0.410\\\hline \rm Time & 0.85 & 1.30 & 1.65\\ \hline\end{array}$$
Use these points to create simultaneous equations of the form $a(x) = Ne^{kx}$, where $N$ represents the maximum height and $k$ represents the corresponding time.
So basically I have to graph the 3 quadratic equations of the 3 bounces of the ball using a combined equation: $Ne^{kx} |\sin(b(x-c))|+d$
The equation $f(x)=|a \sin(b(x-c))|+d$ was used to graph the duration of the 3 bounces. While the $Ne^{kx}$ is supposed to vary the height of each bounce accordingly.