A patient has an illness that typically lasts about 24 hours. The temperature, $ T $, in degrees Fahrenheit, of the patient $ t $ hours after the illness begins is given by:

\[ T(t) = -0.021t^2 + 0.5208t + 98.2 \]

This is a Mathematics problem that involves understanding a quadratic equation which represents a patient's body temperature during an illness. The equation can predict the temperature at any given time, and identify at what point the fever will peak.

Explanation:

The question involves understanding the function T(t)=-0.021t²+0.5208t+98.2 which models the patient's temperature in degrees Fahrenheit over the course of their illness. This function is a quadratic equation, a type of function often used in physical sciences and mathematics to model a wide variety of phenomena, including the patient's body temperature in this case. The function predicts the temperature T at a given time t.

At the start of the illness (when t=0), the body temperature is approximately 98.2 degrees Fahrenheit, represented by the y-intercept in the equation. As time progresses, represented by the t in the function, the body temperature rises and falls in a pattern defined by the equation. The point where fever spikes can be found as the maximum point of the quadratic equation. This can be found using the formula -b/2a of the quadratic equation (ax²+bx+c) which yields the values of t. You can then substitute the value of t into the equation to determine T.

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A patient has an illness that typically lasts about 24 hours. The temperature, \( T \), in degrees Fahrenheit, of the patient \( t \) hours after the illness begins is given by:\[ T(t) = -0.021t^2 + 0.5208t + 98.2 \]

Answer :

Final answer:

Explanation:

Other Questions

A patient has an illness that typically lasts about 24 hours. The temperature, \( T \), in degrees Fahrenheit, of the patient \( t \) hours after the illness begins is given by:

\[ T(t) = -0.021t^2 + 0.5208t + 98.2 \]