Suppose the amount of algae in pond triples every day. After 12 days the pond is complete with algae. I believe that on day 4 the pond is 1/3 of the way full. Am i correct?

Answer 1

What does full mean?

Multiply by 3 every day?

That is called geometric sequence

http://www.mathsisfun.com/algebra/sequences-sums-geometric.html

Say A is amount on day 1
then on day 12 you have
A(3)^11
and on day 4 you have
A(3)^3

3^11/3^3 = 3^8 = 6561

so you have 6561 times as much on day 12 as on day 4

so no, not 1/3 :)