Final answer:
The number of yeast cells in the dish at 7:30 a.m., given an initial count of 10 cells at 7:00 a.m. and a doubling rate every 5 minutes, would be 640 cells. This was calculated using the formula N(t) = N0 * 2^(t/dt) for exponential growth.
Step-by-step explanation:
The question asks for the number of yeast cells in a dish at 7:30 a.m. given an initial population of 10 yeast cells at 7:00 a.m. and assuming an exponential growth rate with a doubling time of 5 minutes.
To find the number of cells at 7:30 a.m. we calculate the number of 5-minute intervals from 7:00 a.m. to 7:30 a.m, which is 6 intervals (30 minutes ÷ 5 minutes per interval).
Since the population doubles every interval, we use the formula for exponential growth:
N(t) = N0 * 2^(t/dt) where N(t) is the number of cells at time t, N0 is the initial number of cells, t is the total time in intervals, and dt is the doubling time in intervals. Using the values N0 = 10 cells, t = 6 intervals, and dt = 1 interval (5 minutes), we get:
N(6) = 10 * 2^6 = 10 * 64 = 640
So, there are 640 yeast cells in the dish at 7:30 a.m.