Suppose that the amount of algae is a pond doubles every 3 hours. If the pond initially contains 70 pounds of algae, how much algae will be in the pond after 9 hours?
Is the answer 560? I was not sure how to set it up, but doubled it every 3 hours. If this is not correct, please show me how to solve.
To solve this problem, we need to understand the pattern of growth. The amount of algae in the pond is doubling every 3 hours.
To find out how much algae will be in the pond after 9 hours, we can break it down into smaller steps.
Step 1: Determine how many times the algae will double in 9 hours.
Since the algae doubles every 3 hours, in 9 hours it will double 9/3 = 3 times.
Step 2: Calculate the final amount of algae.
Starting with 70 pounds of algae, if it doubles 3 times, the final amount would be:
70 pounds (initial amount) * 2 (the first doubling) * 2 (the second doubling) * 2 (the third doubling) = 70 pounds * 2^3 = 70 pounds * 8 = 560 pounds.
So, the correct answer is indeed 560 pounds.
To solve this problem, you can use exponentiation as the amount of algae doubles every 3 hours. Here's the step-by-step solution:
Step 1: Determine the number of times the algae doubles in the given time frame.
Since the algae doubles every 3 hours and you want to find out the amount after 9 hours, divide the total time by the doubling time: 9 hours / 3 hours = 3 times.
Step 2: Use the formula to calculate the final amount of algae:
Final amount = Initial amount * (2^number of doublings)
Step 3: Plug in the values:
Initial amount = 70 pounds
Number of doublings = 3
Final amount = 70 * (2^3)
= 70 * (2 * 2 * 2)
= 70 * 8
= 560 pounds
So, the correct answer is 560 pounds. Well done!
population p = 70*2^(n/3) after n hours
70 * 2^3 = 70*8 = 560