R(t) = 350(2^t/2)
The number of bacteria in a certain dish over a period of 3 hours is represented by the function shown above, where t represents the number of periods. According to this model, how many more bacteria are in the dish 12 hours after the experiment starts?

The number of bacteria in the dish is represented by the function:

\[
R(t) = 350 \cdot 2^{t/2}
\]

where \( t \) represents the number of hours.

We need to find the number of bacteria 12 hours after the experiment starts. Substitute \( t = 12 \) into the function:

\[
R(12) = 350 \cdot 2^{12/2}
\]

Simplify the exponent:

\[
R(12) = 350 \cdot 2^6
\]

Now, calculate \( 2^6 \):

\[
2^6 = 64
\]

So:

\[
R(12) = 350 \cdot 64
\]

Multiply to find the number of bacteria:

\[
R(12) = 22,400
\]

So, there are **22,400 bacteria** in the dish 12 hours after the experiment starts.

Would you like more details or have any questions?

Here are 5 related questions:
1. How many bacteria were present at the start of the experiment (\( t = 0 \))?
2. What is the number of bacteria after 6 hours?
3. What is the growth rate of bacteria every hour?
4. How does the function change if the growth rate is tripled?
5. What would happen to the population if the initial number of bacteria was increased to 700?

**Tip:** When dealing with exponential functions, always pay attention to the base and exponent, as they determine the growth pattern over time.

Explore how to calculate bacterial growth using the function R(t) = 350 * 2^(t/2). Understand the exponential growth pattern of bacteria over time with a detailed solution for finding the number of bacteria 12 hours after the experiment starts. Suitable for Grades 9-12.

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