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 :
Final answer:
The patient's temperature reaches its maximum value after 10.7 hours, where the maximum temperature is approximately 99.7°F. This is determined by finding the vertex of the quadratic function that represents the temperature over time.
Explanation:
To determine the time at which the patient's temperature reaches its maximum value, we need to find the vertex of the given quadratic function.
The equation provided for the temperature T(t) is T(t) = -0.014t² + 0.2996t + 97.7.
We can find the time at which the maximum temperature occurs by using the formula for the vertex of a parabola, which is given by -b/(2a) for a quadratic equation in the form of ax² + bx + c.
In this case, a = -0.014 and b = 0.2996. Plugging these values into the formula gives:
t = -0.2996 / (2 × (-0.014))
= -0.2996 / (-0.028)
= 10.7 hours (rounded to one decimal place).
The maximum temperature can be found by plugging this time back into the original equation:
T(10.7) = -0.014 × (10.7)² + 0.2996 × 10.7 + 97.7
= -0.014 × 114.49 + 3.205252 + 97.7
≈ 99.7°F (rounded to one decimal place).
Therefore, the patient's temperature reaches its maximum value after 10.7 hours with a maximum temperature of approximately 99.7°F.
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Rewritten by : Jeany
