# Conversion of price in different seconds to determine the speed of the fall

I'm having a thought problem. I'm looking for a conversion to determine the speed of the price decrease. e.g if

\begin{align} \$398 & = 120\text{ seconds} \\ \$62 & = 0\text{ seconds} \\ ?? & = 60\text{ seconds} \\ ?? & = 1\text{ second} \end{align}

So I want to know how much the price is at 60 seconds and how much the price is at 1 seconds. Through cross multiplication, I already know that the price decrease is convex but somehow I am having problem to find a solution to this problem. Any idea?

-
If all you have is two measures, then you can only produce a straight line out of it. Ideally, you should have many measures to interpolate an equation that produces more accurate results. How do you know the curve is convex, if you only have two points? – elite5472 Jun 18 '13 at 15:52
Hey you are correct. My specification was wrong. I replotted it with more points and rather got a line! – Dat Tran Jun 19 '13 at 14:11

It looks like the price is increasing, not decreasing. The points are $(120,398)$ and $(0,62)$ If you want a straight line, you can use the two point form for the line, $p$ for price and $t$ for time, it would be $p-62=(398-62)\dfrac {t-0}{120-0}$ where I left the zeros in to show the form. Now plug $1,60$ in for $t$ and you can read off the price. Without some further information about convexity, you can't do any better.

-

I would do the following, P = (398,120), Q = (62,0)

To find the mid point is easy.

S(t) = P+t(Q-P)

S(60/120) = P + .5(Q-P)

S(1/2) = (P + Q)/2 = (230,60)

Then simply repeat the formula for 1/120

S(119/120) = P + (119/120)(Q-P)

(398,120)+(119/120)(-336,-120) = (398-333.2,120-119)=(64.8,1)

Hope that helps.

-