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:

\[ T(t) = -0.014t^2 + 0.322t + 97.3 \]

Round all answers to 1 decimal place.

1. When does the patient's temperature reach its maximum value?
Answer: After hours.

2. What is the patient's maximum temperature during the illness?
Answer: °F.

The patient's temperature reaches its maximum value approximately 11.5 hours after the illness begins. The maximum temperature during the illness is approximately 101.4°F.

To find the maximum temperature during the illness, we need to determine the vertex of the quadratic function representing the temperature.

Tthe equation:

T(t) = -0.014t^2 + 0.322t + 97.3

The vertex of a quadratic function in the form of f(x) = ax^2 + bx + c is given by x = -b / (2a).

In this case, a = -0.014 and b = 0.322.

Calculating the vertex:

t = -0.322 / (2 * (-0.014))

t ≈ -0.322 / (-0.028)

t ≈ 11.5 hours

Therefore, the patient's temperature reaches its maximum value approximately 11.5 hours after the illness begins.

To find the maximum temperature, substitute the value of t into the equation T(t):

T(11.5) = -0.014(11.5)^2 + 0.322(11.5) + 97.3

T(11.5) ≈ 101.4°F

Therefore, the patient's maximum temperature during the illness is approximately 101.4°F.

To know more about temperature,

https://brainly.com/question/7510619#

#SPJ11