A patient has an illness that typically lasts about 24 hours. The temperature, [tex]t[/tex], in degrees Fahrenheit, of the patient [tex]t[/tex] hours after the illness begins is given by:

[tex]t(t) = -0.02t^2 + 0.448t + 97.7[/tex]

What is the temperature of the patient 2 hours after the illness begins?

1) [tex]-0.02(2)^2 + 0.448(2) + 97.7[/tex]

2) [tex]-0.02(2)^2 + 0.448(2) - 97.7[/tex]

3) [tex]-0.02(2)^2 - 0.448(2) + 97.7[/tex]

4) [tex]-0.02(2)^2 - 0.448(2) - 97.7[/tex]

The temperature of the patient 2 hours after the illness begins is calculated using the equation t(t) = -0.02t² + 0.448t + 97.7, yielding a result of 98.516°F.

Explanation:

The temperature of the patient 2 hours after the illness begins can be calculated using the given quadratic equation t(t) = -0.02t² + 0.448t + 97.7. To find the temperature at t = 2 hours, we substitute 2 for t in the equation:

t(2) = -0.02(2)² + 0.448(2) + 97.7

First, calculate the square of 2, which is 4. Then multiply by -0.02: -0.02(4) = -0.08

Next, multiply 0.448 by 2: 0.448(2) = 0.896

Now add these results together and add 97.7 to find the final temperature: -0.08 + 0.896 + 97.7 = 98.516

Therefore, the temperature of the patient 2 hours after the illness begins is 98.516°F.