Final answer:
The minimum number of bacteria, based on the given function, occurs at a temperature of 0.5 degrees Celsius, which is found by calculating the vertex of the parabola.
Step-by-step explanation:
To determine the temperature at which the number of bacteria will be minimal based on the given quadratic function N(t) = 20x² - 20x + 120, we need to find the vertex of this parabola. The formula for finding the x-coordinate of the vertex of a quadratic function in the form ax² + bx + c is -b/(2a). In this instance, a = 20 and b = -20, so the x-coordinate for the vertex will be -(-20)/(2*20) = 0.5. Since the coefficient of the x² term is positive, this means that the graph of the function opens upwards and the vertex represents the minimum point of the graph.
Therefore, the minimum number of bacteria occurs at a temperature of 0.5 degrees Celsius.
It's important to note that this result is realistic and falls within the known biological constraints for bacterial growth, which is usually slower at cooler temperatures as indicated by guidelines for refrigeration and freezing to control microbial growth.