Harriet is cultivating a strain of bacteria in a petri dish. Currently, she has 103 bacteria in the dish. The bacteria divide every two hours such that the number of bacteria has doubled by the end of every second hour. How many bacteria will Harriet have in the dish at the end of 6 hours?

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.

Learn how to calculate bacteria growth over time using exponential growth formula. Solve a problem where bacteria double every 2 hours starting with 103 bacteria. Explore related questions on exponential growth in biological and financial models. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation