Answer :
Final answer:
The question is mathematical and deals with a patient's body temperature over a time period of 24 hours. The temperature is given as a quadratic equation of time 't' hours after the illness begins. Using this equation, one can calculate the patient’s temperature at different times during the illness.
Explanation:
The subject of this question is a mathematical problem dealing with a patient's body temperature over a period of 24 hours when they are experiencing an illness. The temperature T, in degrees Fahrenheit, is represented by the quadratic equation T(t)=-0.029t²+0.6206t+97.3, where t is the time after the illness begins in hours. In this equation, -0.029t² signifies the change in temperature due to the illness which is a decreasing function of time, 0.6206t signifies an initial increase in temperature when the illness begins, and the constant 97.3 represents the patient's normal body temperature in Fahrenheit.
At the start of illness (t=0), the body temperature would be 97.3 F according the equation. By substituting different values for 't' in the equation, we can get the patient's temperature at different hours. For example, at t=12 hours, the patient's temperature according to the equation is T(12) = -0.029*(12²) + 0.6206*12 + 97.3, which rounds to 99.5 degrees Fahrenheit when rounded to 1 decimal place.
This equation can be key in determining the severity of the patient's fever at any point during the 24 hours. Additionally, comparing the temperatures derived from this equation to the normal body temperature range of 97 to 99 degrees Fahrenheit could provide useful information about the patient's health condition during the illness. It should be noted that this equation is a simplification and actual body temperature can vary due to many factors, including individual differences, time of day, and activity level.
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