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To solve this problem, we need to find out how the number of Salmonella bacteria changes after the food has been removed from refrigeration.

### Given:
1. The number of Salmonella bacteria at temperature \( x \) (in degrees Celsius) is given by:
   \[
   n(x) = 15x^2 - 87x + 789, \quad \text{for } 7 \leq x \leq 46.
   \]

2. The temperature \( x(t) \) after \( t \) minutes of removing the food from the refrigerator is given by:
   \[
   x(t) = 3t + 4, \quad \text{for } 0 \leq t \leq 7.
   \]

### Steps to solve:

1. **Formulate an equation for the number of Salmonella bacteria as a function of time \( t \):**

   The temperature after \( t \) minutes is \( x(t) = 3t + 4 \). Substitute this into the function for \( n(x) \):

   \[
   n(x(t)) = 15(3t + 4)^2 - 87(3t + 4) + 789.
   \]

   Simplify this to find the expression for the number of bacteria as a function of \( t \).

2. **Find the number of bacteria 6 minutes after removal from refrigeration:**

   Substitute \( t = 6 \) into the expression for \( n(x(t)) \) to find the number of bacteria at that specific time.

Let's compute the simplified function \( n(x(t)) \) and the number of bacteria after 6 minutes. 

### Calculation:

Substitute \( x(t) = 3t + 4 \) into \( n(x) \):

\[
n(x(t)) = 15(3t + 4)^2 - 87(3t + 4) + 789.
\]

Now, let's expand and simplify this expression.The number of Salmonella bacteria as a function of time \( t \) after the food is removed from refrigeration is:

\[
n(x(t)) = 135t^2 + 99t + 681.
\]

After 6 minutes, the number of Salmonella bacteria is:

\[
n(x(6)) = 6135.
\]

### Conclusion:
There are 6,135 Salmonella bacteria present in the food 6 minutes after it has been removed from the refrigerator.

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Would you like to know more details or have any specific questions? Here are some related questions:

1. How does the growth rate of Salmonella bacteria change with temperature?
2. What would be the number of bacteria after 3 minutes?
3. How to find the maximum number of bacteria within the given time frame?
4. Can you explain how refrigeration impacts bacterial growth mathematically?
5. What happens to the bacterial count if the rate of temperature change is different?

**Tip:** Understanding how temperature affects bacterial growth can be crucial in fields like food safety and microbiology.

Salmonella is a type of bacteria in food that increases in number as the temperature rises. Its growth is slowed down significantly when food is refrigerated. The number of these bacteria in a certain food is a function of the food’s temperature. Refrigeration helps to inhibit the bacteria’s growth and multiplication. When refrigerated, the number of bacteria at temperature x degrees Celsius is described by the function n(x) = 15x^2 - 87x + 789 for 7 ≤ x ≤ 46. When the food is removed from the refrigerator, the temperature increases, and after t minutes, the temperature is x(t) = 3t + 4 for 0 ≤ t ≤ 7. Formulate an equation that shows how the number of Salmonella bacteria changes t minutes after the food has been removed from refrigeration. How many Salmonella bacteria are present in the food 6 minutes after it has been removed from the refrigerator?

Learn how to solve a quadratic function modeling Salmonella bacteria growth based on temperature changes after food is removed from refrigeration. This step-by-step guide explains how to substitute temperature functions into bacterial growth models to calculate bacterial count after a given time. Suitable for students in Grades 10-12.

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