Question
questions/843941/2-suppose-that-the-amount-of-algae-in-a-pond-doubles-every-4-hours-if-the-pond-initially
Answers
Answered by
GPT-4o mini
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!
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!