In a lab experiment, 3100 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 26 hours. How many bacteria would there be after 12 hours, to the nearest whole number?

The number of bacteria grows exponentially, doubling every 26 hours. We can model the bacteria population using the exponential growth formula:

\[
N(t) = N_0 \cdot 2^{\frac{t}{T}}
\]

Where:
- \( N(t) \) is the number of bacteria at time \( t \) hours.
- \( N_0 \) is the initial number of bacteria (3100 in this case).
- \( t \) is the time in hours.
- \( T \) is the doubling time (26 hours in this case).

In this problem, we want to find the number of bacteria after \( t = 12 \) hours.

\[
N(12) = 3100 \cdot 2^{\frac{12}{26}}
\]

Let's compute this step-by-step:

\[
N(12) = 3100 \cdot 2^{\frac{12}{26}} \approx 3100 \cdot 2^{0.4615}
\]

\[
N(12) \approx 3100 \cdot 1.378
\]

\[
N(12) \approx 4272.07
\]

Rounding to the nearest whole number:

\[
N(12) \approx 4272
\]

Thus, after 12 hours, there would be approximately **4,272** bacteria.

Would you like more details or have any questions?

Here are 5 related questions to expand on this:
1. How many bacteria would there be after 26 hours?
2. How would you calculate the number of bacteria after 50 hours?
3. If the doubling time changes to 20 hours, how many bacteria would there be after 12 hours?
4. What would be the initial number of bacteria if there are 6200 bacteria after 26 hours?
5. How long would it take for the bacteria to reach 10,000?

**Tip**: In exponential growth problems, the base of the exponent (in this case, 2) represents the growth factor, and the exponent captures how many times this factor applies over the time period.

Explore how to calculate the population of bacteria using exponential growth. In this example, 3100 bacteria double every 26 hours. Find out how many bacteria would be present after 12 hours using the formula N(t) = N0 * 2^(t/T). Suitable for Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation