The problem in the image seems to be related to bacterial growth over time. It describes a scenario where the population of bacteria increases from 1000 to 1500 in 30 minutes, and then doubles every 45 minutes.

Let's break down the problem:

Câu 3:

Một loại vi khuẩn sau 30 phút thì tăng từ 1000 đến 1500 và cứ gấp đôi sau mỗi 45 phút.

a) Thời gian sau 30 tiếng sau có bao nhiêu con?

b) Mất bao lâu để có 1 tỷ con?

Part (a): Bacterial population after 30 hours

• Initially, there are 1000 bacteria.
• After 30 minutes, the population increases to 1500.
• After every 45 minutes, the population doubles.

We need to calculate the bacterial population after 30 hours (or 1800 minutes).

Part (b): Time to reach 1 billion bacteria

• We need to calculate how long it will take for the bacteria population to reach 1 billion (or 1,000,000,000).

I'll solve both parts step-by-step. Let me calculate it.### Solutions:

Part (a):
After 30 hours, the bacterial population will be approximately 1.04 trillion bacteria (1,038,949,378,224 bacteria).

Part (b):
It will take approximately 14.95 hours (or about 15 hours) for the bacteria population to reach 1 billion.

Would you like further clarification or detailed steps for any part of the solution?

Here are 5 questions that build on this topic:

1. How would the population change if the bacteria took longer to double?
2. What is the formula for exponential growth and how is it applied here?
3. How does changing the initial population affect the time to reach 1 billion?
4. Can this model be applied to other biological growth processes, and how?
5. What are the limitations of using an exponential model for bacterial growth in real-life scenarios?

Tip: When dealing with exponential growth problems, always identify the doubling time and initial values, as they are crucial for calculating future population sizes.