Final answer:
To find the number of days it takes for a water lily population to double, commonly referred to as D, one would solve the equation 7.830 = 3.915(2)D, which models the doubling of the initial population after D days. This task involves understanding exponential growth and may employ the use of logarithms for more precise calculations.
Step-by-step explanation:
To find D, the number of days it takes the water lily population to double, you would need to solve equations that represent the doubling of a quantity. The original value represents the population size at some initial time, and the double of that value represents the population size after doubling. Given the context of doubling times and the provided equations, we must assess which of them correctly represents the concept of doubling.
The equation representing the doubling should start with the original population and result in twice that amount after a certain number of days, D. Therefore, the correct equation would be:
7.830 = 3.915(2)D
Since 3.915(2) represents the original population multiplied by 2, which would be the population doubled. None of the other options show a proper doubling, as they either do not result in the population being multiplied by 2 or they alter the initial population size.
Another approach is to use logarithms to find the doubling time through equations that relate the rate of growth and the doubling time. This method is often more accurate and aligns with the concept of exponential growth through the rule of 70 or the detailed calculation using
t2 = ln 2/ln(1 + p).
Here, p represents the rate of growth. For a small growth rate, this formula often simplifies to 70/p which is known as the rule of 70.