We appreciate your visit to 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. 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 :
The patient's temperature reaches its maximum value approximately 11.5 hours after the illness begins. The maximum temperature during the illness is approximately 101.4°F.
To find the maximum temperature during the illness, we need to determine the vertex of the quadratic function representing the temperature.
Tthe equation:
T(t) = -0.014t^2 + 0.322t + 97.3
The vertex of a quadratic function in the form of f(x) = ax^2 + bx + c is given by x = -b / (2a).
In this case, a = -0.014 and b = 0.322.
Calculating the vertex:
t = -0.322 / (2 * (-0.014))
t ≈ -0.322 / (-0.028)
t ≈ 11.5 hours
Therefore, the patient's temperature reaches its maximum value approximately 11.5 hours after the illness begins.
To find the maximum temperature, substitute the value of t into the equation T(t):
T(11.5) = -0.014(11.5)^2 + 0.322(11.5) + 97.3
T(11.5) ≈ 101.4°F
Therefore, the patient's maximum temperature during the illness is approximately 101.4°F.
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