(Video Ruangguru)- ruangbelajar - Matematika SMA - Barisan dan Deret | bimbel online

Summary

The video explains the exponential growth of bacteria over a 24-hour period. Starting with one bacterium, it divides every 3 hours into 4 new bacteria. This process continues, with the number of bacteria multiplying by four each time. After 8 divisions (3 hours each), the total number of bacteria reaches 65,536. The video provides a clear and easy-to-follow demonstration of how exponential growth works, emphasizing the rapid increase in bacterial population over the course of one day.

Takeaways

• 😀 Bacteria initially start with a single bacterium at time zero.
• 😀 Every 3 hours, the single bacterium divides into 4 bacteria, increasing the total count.
• 😀 After the first 3 hours, 1 bacterium becomes 4 bacteria.
• 😀 After the second 3-hour period, the 4 bacteria each divide into 4, resulting in 16 bacteria.
• 😀 The process of bacterial division happens every 3 hours for the entire 24-hour period.
• 😀 In total, bacteria will divide 8 times in 24 hours (since 24 ÷ 3 = 8).
• 😀 The formula for calculating the total number of bacteria after 8 divisions is 1 × 4^8.
• 😀 4^8 equals 65,536, which is the total number of bacteria after 24 hours.
• 😀 The bacterial population grows exponentially, with each division multiplying the bacteria by 4.
• 😀 The process described in the video helps understand exponential growth in biological systems.

Q & A

How does the bacterial growth process begin in the script?

The bacterial growth begins with one bacterium. After 3 hours, this single bacterium divides into 4 bacteria.

What happens after the first 3-hour period in the script?

After the first 3-hour period, the 1 bacterium divides into 4, resulting in a total of 4 bacteria.

What is the total number of bacteria after the second 3-hour period?

After the second 3-hour period, each of the 4 bacteria divides into 4, resulting in 16 bacteria in total.

How does the bacterial growth pattern continue?

The bacterial growth continues with each bacterium dividing into 4 every 3 hours. The number of bacteria multiplies exponentially by a factor of 4 with each division.

How many divisions occur in 24 hours?

In 24 hours, the bacteria divide 8 times, since each division takes place every 3 hours.

How do you calculate the total number of bacteria after 8 divisions?

To calculate the total number of bacteria after 8 divisions, the formula is 1 × 4^8, which equals 65,536 bacteria.

What is the formula used to determine the total number of bacteria after multiple divisions?

The formula used is N = 4^n, where N is the total number of bacteria, and n is the number of divisions.

Why is the number of bacteria increasing exponentially?

The number of bacteria increases exponentially because each bacterium divides into 4, which means the total number of bacteria multiplies by a factor of 4 every 3 hours.

What does '4^8' represent in the context of the bacterial growth?

In the context of bacterial growth, '4^8' represents the total number of bacteria after 8 divisions, calculated by multiplying the initial number of bacteria (1) by 4 raised to the power of 8.

How can the concept of exponential growth be applied to other areas of biology or science?

Exponential growth, like bacterial division, is commonly observed in populations of organisms, viruses, and other biological systems. It shows how rapidly a population can increase under ideal conditions, where resources are abundant and there are no limiting factors.