We appreciate your visit to A patient has an illness that typically lasts about 24 hours The temperature tex T tex in degrees Fahrenheit of the patient tex t tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The vertex of the given quadratic equation, which represents the peak temperature of a patient's illness, occurs roughly 12 hours into the illness and reaches a temperature of around 98.1°F.
Explanation:
The equation given represents a parabola, and its vertex can be found using the formula: h=-b/2a , where a and b are coefficients of the quadratic equation (in this case, a = -0.022, b = 0.528). Thus, the t-coordinate of the vertex (h) is -(0.528) / 2*(-0.022) which results in approximately 12 hours. To find the temperature at the vertex (k), substitute h into the equation: T(12) = -0.022*12^2 + 0.528*12 + 97.7 which gives about 98.1°F. Hence, the vertex of the parabola is (12, 98.1), meaning the patient's temperature will be at its peak 12 hours into the illness and will reach approximately 98.1°F.
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