Bacteria cannot live at temperatures higher than 120 f. using the inequality below, solve for c to determine the temperatures in degrees celsius in which bacteria cannot survive.
The Correct Answer and Explanation is:
To solve this problem, we need to convert the temperature of 120°F into Celsius and understand the relationship between Fahrenheit (°F) and Celsius (°C).
Step 1: Understanding the Inequality
The inequality you have is describing the condition in which bacteria cannot survive if the temperature exceeds 120°F. We will use the conversion formula between Fahrenheit and Celsius to convert this temperature.
The general formula for converting Fahrenheit (°F) to Celsius (°C) is:
[
C = \frac{5}{9} (F – 32)
]
Where:
- (C) is the temperature in degrees Celsius.
- (F) is the temperature in degrees Fahrenheit.
Step 2: Converting 120°F to Celsius
Now, we will substitute (F = 120) into the formula:
[
C = \frac{5}{9} (120 – 32)
]
[
C = \frac{5}{9} \times 88
]
[
C = \frac{440}{9}
]
[
C \approx 48.89
]
So, 120°F is approximately 48.89°C.
Step 3: Interpreting the Answer
Since the bacteria cannot live at temperatures higher than 120°F, we can say that the maximum temperature at which bacteria can survive is 48.89°C. Therefore, the temperatures in Celsius where bacteria cannot survive are those greater than 48.89°C.
Final Answer:
Temperatures greater than approximately 48.89°C are too hot for bacteria to survive.
Explanation:
The relationship between Fahrenheit and Celsius is linear, but we must use the conversion formula to accurately translate temperatures between the two scales. By converting 120°F to Celsius, we found that temperatures above 48.89°C are unsafe for bacterial survival. This is important in microbiology, where temperature control is essential to prevent bacterial growth.