To calculate the number of bacteria after one day, given that the bacteria double every 6 hours, we can use the exponential growth formula:

$N(t) = N_0 \cdot 2^{t/T}$

Where:

• $N(t)$ is the number of bacteria at time $t$,
• $N_0$ is the initial number of bacteria,
• $t$ is the elapsed time (in hours),
• $T$ is the doubling time (in hours).

Given:

• $N_0 = 1000$,
• $T = 6 \, \text{hours}$,
• $t = 24 \, \text{hours (1 day)}$.

Solution:

$N(24) = 1000 \cdot 2^{24/6}$ $N(24) = 1000 \cdot 2^4$ $N(24) = 1000 \cdot 16$ $N(24) = 16000$

Final Answer:

After one day, there will be 16,000 bacteria.

Would you like me to explain exponential growth further or answer related questions?

Related Questions:

1. What if the doubling time was 3 hours instead of 6 hours?
2. How would the formula change if the growth was continuous instead of discrete?
3. How many bacteria would there be after 30 hours?
4. Can you calculate the time it would take for the bacteria count to reach 50,000?
5. What if the initial count was 500 instead of 1000?

Tip: In problems involving growth or decay, always identify the doubling or halving period first for clarity.