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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