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:

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

a. When does the patient's temperature reach 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.

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:\[ T(t) = -0.025t^2 + 0.615t + 98.2 \]a. When does the patient's temperature reach its maximum value?

Answer :

Other Questions

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:

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

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