Thank you for visiting 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 is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The patient's temperature reaches its maximum value after 12.1 hours of the illness. The patient's maximum temperature during the illness is about 100.1°F.
The given function is:
T(t) = -0.017t² + 0.4114t + 97.8.
A patient has an illness that typically lasts about 24 hours. Therefore, the value of t ranges from 0 to 24. Using a graphing calculator, The maximum value of a quadratic function occurs at the vertex of the parabolic graph, which is located at
t = - b / 2a
The value of 'a' is -0.017 and the value of 'b' is 0.4114.
Hence,
t = - 0.4114 ÷ 2(-0.017)
= 12.1 hours
after the illness begins is when the patient's temperature reaches its maximum value.
The maximum temperature of the patient during the illness is:
T(12.1) = -0.017(12.1)² + 0.4114(12.1) + 97.8
≈ 100.1°F
You can learn more about the temperature at: brainly.com/question/11464844
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