00:02
Water is approximated by the logistic function g of t.
00:05
We need to find the derivative of it, and then we can use the derivative function to find the growth rate in five years.
00:16
So we want to find ddt of 37 ,500 over 14e to the negative, i'm going to call it 16t over 25 plus 1, which would be equal to 37 ,000.
00:37
500 times d d t of 1 over 14 e to the negative 16 t over 25 plus 1 which would be negative 37 500 times d d t of 14 e to the negative 16 25 plus 1 over 14 e to the negative 16 25s t plus 1 over 14 e to the negative 16 25th t plus one squared, which would be negative 37 ,500 times 14 d, d .t of e to the negative 1625th t plus d, dt of 1 over 14e to the negative 1625th t, plus ddt of 1 over 14e to the negative 1625th t.
02:00
Plus 1 squared, which would be negative 37 ,500 times 14e to the negative 16t over 25 times ddt of negative 16t over 25 plus 0 over 14e to the negative 16 25 plus 0 over 14 e to the negative 16 25th t plus 1 squared.
02:37
And some simplifying now, that would be 52 ,000, or not 52 ,000, but 525 ,000 times negative 16, 25ths, times d, dt of t, times e to the negative 16, 25th's t...