Final answer:
To calculate bacterial growth after 80 minutes and 10 hours, we use the exponential growth formula N = N0 x 2^t, where N0 is the initial number of bacteria and t is the number of doubling periods within the given time frame.
Step-by-step explanation:
Calculating Bacterial Population Growth
To determine the size of a bacterial population after a certain amount of time, we need to use an exponential growth model. Given that the bacteria culture doubles every half hour, we can calculate the number of bacteria after any given period by identifying the number of half-hour intervals in that time frame.
For example, after 80 minutes, there are ⅓ hour (50 minutes) plus 30 minutes, which totals to 2.67 half-hour intervals (80 minutes / 30 minutes per interval). To find out the size of the population after 80 minutes, we would use the formula:
N = N0 × 2t
Where:
- N is the final population size,
- N0 is the initial population size,
- t is the number of doubling times,
Plugging the numbers into the formula, we get:
N = 1500 bacteria × 22.67
This results in an approximate count of bacterial population after 80 minutes.
To calculate the population after 10 hours (which is 20 half-hour intervals), we can use the same formula with t as 20:
N = 1500 bacteria × 220
This will give the size of the bacterial population after 10 hours.
It's important to note that the exponential growth model shows how populations increase at a greater rate with each doubling period, creating a J-shaped growth curve.