High School

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 begins is given by:

\[ T(t) = -0.025t^2 + 0.615t + 98.2 \]

Use your calculator to graph the function and answer the following question. Round all answers to one decimal place.

When does the patient's temperature reach its maximum value?

Answer: ______

Answer :

Final answer:

The patient's temperature reaches its maximum value 12.3 hours after the illness begins.

Explanation:

To determine when the patient's temperature reaches its maximum value, we need to find the vertex of the quadratic function. The vertex of a quadratic function in the form y = ax^2 + bx + c is given by the formula x = -b/2a.

In this case, the quadratic function is T(t) = -0.025t^2 + 0.615t + 98.2. We can see that a = -0.025 and b = 0.615. Plugging these values into the formula, we get x = -0.615 / (2 * -0.025) = 12.3.

Therefore, the patient's temperature reaches its maximum value 12.3 hours after the illness begins.

Learn more about maximum value of a quadratic function here:

https://brainly.com/question/30318138

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