Final answer:
The population size of a yeast cell with an initial number of 3.3 million cells and a growth rate of 0.4427 per hour after 3 hours is approximately 12.4 million cells. So, the answer is not in the options, try checking the question again.
Step-by-step explanation:
The student asked to find the population size of a yeast cell after 3 hours given a constant relative growth rate of 0.4427 per hour and an initial population of 3.3 million cells. To calculate this, we can use the formula for exponential growth:
N(t) = N₀eʳᵗ
Where N(t) is the population size at time t, N₀ is the initial population size, r is the growth rate, and t is time in hours.
Here, N₀ = 3.3 million, r = 0.4427, and t = 3 hours. Plugging in these values we get:
N(3) = 3.3e⁽⁰.⁴⁴²⁷⁾⁽³⁾
N(3) = 3.3e¹.³²⁸¹
Using a calculator to find the value of e raised to 1.3281 and then multiplying by 3.3, we find:
N(3) ≈ 3.3 × 3.7642
N(3) ≈ 12.42186 million cells
After rounding to one decimal place, the population size after 3 hours is approximately 12.4 million cells.
Therefore, the answer is not in the options, try checking the question again.