Final answer:
The daily growth rate of a weed species that triples in 6 days is approximately 18.77%, calculated using the exponential growth formula with the initial and final amounts and the time period.
Step-by-step explanation:
To calculate the daily growth rate of a weed species that triples in 6 days, we'll use the exponential growth formula:
A = P(1 + r)^t
Where A is the amount after time t, P is the initial amount, r is the growth rate, and t is the time.
Since the weed triples in 6 days, our formula will be:
36 = 12(1 + r)^6
To find the daily growth rate, we solve for r:
(1 + r)^6 = 3
(1 + r) = 3^(1/6)
r = 3^(1/6) - 1
After calculating the sixth root of 3 and subtracting 1, we get:
r = 0.1877
Therefore, the daily growth rate is approximately 18.77% per day.