/ck/ - Food & Cooking

>>14941642
x' = Ax, where A is tbd.
Employing separation of variables and integrating , we get:
ln(x) = At + C, where C is our integration constant. Solving for x, we get:
x(t) = e^(At+C) = Be^At, where B is e^C. Now at t=0

x(0)=B, so B is our initial lilypads, so let B=1 for simplicity, and we have that:

x(t)=e^At. We know the population doubles each day, so therefore:
2x=e^A(t+1), and so e^A(t+1) = 2e^At. Doing some rearranging, we have that:
1/2 = e^At/(e^A(t+1) => 1/2 = e^-A => -ln(1/2) = A.
So x(t) = e^-ln(1/2)t.

Finally, solving for when the lake is half full, 1/2 = e^-ln(1/2)t/(e^-48ln(1/2)). Rearranging, we have:
1/2 = e^ln(1/2)(48-t) => ln(1/2)=ln(1/2)(48-t) =>1=48-t => t=47.

>>8937310
A simian based soup?

>>8906966