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 :
a. At 12.3 hours, the patient's temperature reaches its maximum value.
To determine when the patient's temperature reaches its maximum value, we need to find the vertex of the parabolic function T(t) = -0.025t² + 0.615t + 98.2.
For a quadratic function T(t) = at² + bt + c, the vertex, which gives the maximum (or minimum) value, occurs at t = -b/(2a).
Given:
- a = -0.025
- b = 0.615
The time t when the temperature reaches its maximum is:
t = -b / (2a)
t = -0.615 / (2 * -0.025)
t = -0.615 / -0.05
t = 12.3
So, the patient's temperature reaches its maximum value 12.3 hours after the illness begins.
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