To solve the problem, we need to determine the number of bacteria in the dish after 6 hours. Given that the bacteria double every 2 hours, we can use the formula for exponential growth:

$N(t) = N_0 \times 2^{\frac{t}{T}}$

Where:

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

Given:

• $N_0 = 103$ bacteria,
• $T = 2$ hours,
• $t = 6$ hours.

Now, we plug in the values:

$N(6) = 103 \times 2^{\frac{6}{2}}$

$N(6) = 103 \times 2^3$

$N(6) = 103 \times 8$

$N(6) = 824$

So, Harriet will have 824 bacteria in the dish at the end of 6 hours.

Would you like to explore any more details or have any questions?

Here are 5 related questions:

1. What would be the number of bacteria after 8 hours?
2. How many bacteria will there be after 10 hours?
3. What if the bacteria divided every 3 hours instead? How would this affect the number after 6 hours?
4. How many hours will it take for the bacteria to reach 1,000,000?
5. If Harriet started with 200 bacteria, how many would there be after 6 hours?

Tip: Understanding exponential growth is crucial for many biological and financial models. The concept applies whenever something doubles at regular intervals.