Question

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) = -0.02t² + 0.448t + 97.7. What is the temperature of the patient 2 hours after the illness begins?

1) -0.02(2)² + 0.448(2) + 97.7
2) -0.02(2)² + 0.448(2) - 97.7
3) -0.02(2)² - 0.448(2) + 97.7
4) -0.02(2)² - 0.448(2) - 97.7

Answer 1

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.

Step-by-step 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.