Suppose the amount of algae in a pond doubles every 3 hours. If the pond initially contains 50 pounds of algae how much algae will be in the pond after 8 hours
To find out how much algae will be in the pond after 8 hours, we need to use the fact that the amount of algae doubles every 3 hours.
First, let's calculate how many times the algae will double in 8 hours. Since the algae doubles every 3 hours, there are 8 hours divided by 3 hours per doubling, which gives us 2.67 doublings.
Next, we calculate the final amount of algae by multiplying the initial amount of algae (50 pounds) by 2 raised to the power of the number of doublings (2.67). Mathematically, it can be represented as:
Final amount of algae = Initial amount of algae * (2^number of doublings)
Plugging in the values:
Final amount of algae = 50 * (2^2.67)
Now, let's calculate 2^2.67:
2^2.67 ≈ 7.97
Finally, we can calculate the final amount of algae:
Final amount of algae = 50 * 7.97 ≈ 398.37 pounds
Therefore, after 8 hours, there will be approximately 398.37 pounds of algae in the pond.
the amount after t hours is
50*2^(t/3)
So plug in t=8