Zach Read

Got interested in statistics - began trying to extrapolate the amount of minutes Mikey Moore will play tonight. First 5 Tottenham games, he played 0 minutes. This simply a line of y=0. Next 3 Tottenham games, he played 2 minutes, followed by 5, followed by 14. So simply, we can create an exponential growth model by using the coordinates (5,2), (6,5), and (7,14). We can use the equation y=ae^(b(x−4))+c to figure out an appropriate exponential equation. We have to use x-4 to account for the fact that this growth starts after the 5th game (or here, the y=4 coordinate, since we started graphing at 0). Using a system of equations, we can substitute each coordinates into the y and x to get 3 different equations: 1. 2=ae^b+c 2. 5=ae^(2b)+c 3. 14=ae^(3b)+c From here, we do the simple solving for C by equating 2 of the equations to each other. We then subtract the 1st equation from the 2nd to get 3=a(e^b)((e^b)−1), and the 3rd from the 2nd to get 9=a(e^2b)((e^b)−1). Since we have successfully eliminated c, we need to eliminate one more variable, and we can eliminate a by dividing the 2nd equation we got by the 1st. This will leave us with 9/3 = a(e^2b)((e^b)−1)/3=a(e^b)((e^b)−1). First half of the equation is smiply 3, the first term of the 2nd half will become e^b as the a term disappears, whilst we subtract the indicies. The 2nd term of the 2nd half will also disappear. So we 3=e^b. And we can use natural logarithms to solve for b, meaning b is simply ln3. Now is the easy the part, we have b, so we can just substitute ln3 into the first equation that we got via subtraction. 3=a(e^b)(e^b−1) which becomes 3=a(e^ln3)((e^ln3)-1). e to the ln3 is simply just 3, so this becomes easy. 3=a(3)(2) so we have 3=6a which means a = 1/2. Finally, we can work out c, which is done by substituting b and a into the original equations. Any of them. To save you boredom, I will tell you I arrived at c=1/2. Now we can substitue our values to get a value for the curve that we can use to extrapolate Mikey Moore's minutes. y=1/2(e^((ln3))(x-4)))+1/2, which can be simplified to y=1/2(3^(x-4))+1/2. So, I decided to plot this on Desmos. Based on extrapolation, I predict Mikey Moore to see 41 minutes vs. Ferencvaros.

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