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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.

Nam Truong
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  • is $N>0$ or how can an exponential function be negative? – Dr. Sonnhard Graubner Oct 03 '14 at 17:56
  • A ball was dropped from point '0' and it landed on the ground at -0.524m. Meaning the height of the drop was 52.4cm. The ball then bounced up to -0.277m, meaning it bounced up 0.247m. – Nam Truong Oct 04 '14 at 00:47
  • It seems to me that you should find a new displacement of the height, perhaps using that $f_{max}=a+d$? – Lehs Oct 04 '14 at 01:17
  • Thanks for your consideration. I am not too sure about that either, on the question it does not state which to use. Sorry – Nam Truong Oct 04 '14 at 01:31

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