Final answer:
To find when two species with different doubling times will have the same mass, set up an equation using the exponential growth formula and solve for time. It will take approximately 19 hours for Species A and B to have the same mass.
Step-by-step explanation:
The student is asked to determine the time it will take for two species with different growth rates to reach the same mass. Species A, starting with 7 grams, doubles every 3 hours. Species B, starting with 15 grams, doubles every 6 hours. We're looking for the point where their masses are equal.
To solve this problem, we use the formula for exponential growth: Final Mass = Initial Mass × (2^(Elapsed Time / Doubling Time)). Let's denote the number of hours it takes for both species to have the same mass as 't'. For Species A: Final Mass = 7 × (2^(t/3)). For Species B: Final Mass = 15 × (2^(t/6)).
Equating the two gives us:
7 × (2^(t/3)) = 15 × (2^(t/6))
To find the value of 't', we need to solve this equation. By dividing both sides by 7 and then taking the logarithm of both sides, we eventually find that t is approximately 18.9626 hours. Thus, it will take just under 19 hours for both species to reach the same mass.