p(x) = 90 / (9 + 50 * e^(-x))
e = 2.718, so we can use e = 2.7 as a quick substitute
p(3) =>
90 / (9 + 50 * e^(-3)) =>
90 / (9 + 50 * 2.7^(-3)) =>
90 / (9 + 50 / 2.7^3) =>
90 / ((9 * 2.7^3 + 50) / 2.7^3) =>
90 * 2.7^3 / (9 * 2.7^3 + 50)
2.7^3 =>
(27/10)^3 =>
27^3 / 1000 =>
729 * 27 / 1000 =>
2187 * 9 / 1000 =>
6561 * 3 / 1000 =>
19683 / 1000 =>
19.683
90 * 2.7^3 / (9 * 2.7^3 + 50) =>
90 * 19.683 / (9 * 19.683 + 50)
9 * 19.683 =>
9 * (20 - 0.317) =>
180 - 9 * 0.317 =>
180 - 9 * 0.3 - 9 * 0.017 =>
180 - 2.7 - 9 * 0.01 - 9 * 0.007 =>
177.3 - 0.09 - 0.063 =>
177.3 - 0.153 =>
177.15 - 0.003 =>
177.147
90 * 19.683 / (9 * 19.683 + 50) =>
10 * 177.147 / (177.147 + 50) =>
1771.47 / 227.147 =>
1771470 / 227147 =>
1770000 / 225000 =>
1770/225 =>
4 * 1770 / 900 =>
4 * 177 / 90 =>
708/90 =>
70.8 / 9 =>
23.6 / 3 =>
(21 + 2.6) / 3 =>
7 + 0.866666.... =>
7.8666666...
Actual value: 7.8333389811057471507345888320992.....
Not bad for some estimates, is it?