questions/843941/2-suppose-that-the-amount-of-algae-in-a-pond-doubles-every-4-hours-if-the-pond-initially

1 answer

It looks like you're referencing a specific scenario about algae growth in a pond. Based on your description, if the amount of algae doubles every 4 hours, we can express its growth mathematically.

Let's denote the initial amount of algae in the pond as \( A_0 \).

After \( t \) hours, the amount of algae can be calculated using the formula:

\[ A(t) = A_0 \cdot 2^{(t/4)} \]

where:

  • \( A(t) \) is the amount of algae at time \( t \).
  • \( A_0 \) is the initial amount of algae.
  • \( (t/4) \) is the number of 4-hour intervals that have passed.

Example Calculation

If you have an initial amount of algae, say \( A_0 = 10 \) units, and you'd like to determine the amount after 12 hours:

\[ A(12) = 10 \cdot 2^{(12/4)} = 10 \cdot 2^3 = 10 \cdot 8 = 80 \]

So, after 12 hours, there would be 80 units of algae in the pond.

If you have a specific question or if you'd like to explore different aspects of this scenario, please provide more details!