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?
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 :)
To answer this question, we need to understand the exponential growth pattern of the algae in the pond.
According to the given information, the amount of algae in the pond triples every day. This means that if we start with an initial amount of algae (let's say 1 unit), it will triple each day: Day 1: 1 unit, Day 2: 3 units, Day 3: 9 units, Day 4: 27 units, and so on.
To determine whether the pond is 1/3 full on day 4, we can calculate the total amount of algae on that day.
Starting with 1 unit, the amount of algae on day 4 would be 1 unit × 3^3 (since it triples three times):
1 unit × 3 × 3 × 3 = 1 unit × 27 = 27 units
Therefore, on day 4, the pond would contain 27 units of algae, which is not 1/3 of the total amount. Thus, your belief that the pond is 1/3 full on day 4 is incorrect.