Question

Assume that the temperature T, in degrees Fahrenheit, of a patient t days into a 12-day illness is given by

T(t)=100.3°+6°sin(π/8 t)
Find the times t during the illness at which the patient's temperature was 103° is ___

Answer 1

To find the times when the patient's temperature was 103°F, we set up an equation using the given temperature function, then solve for the variable t that represents days. The solutions for t are approximately 1.07 days and 10.96 days within the 12-day illness period.

Step-by-step explanation:

To solve for the times t during the illness at which the patient's temperature was 103°F, we need to set T(t) = 103°F and solve for t.

The given function for temperature is T(t) = 100.3° + 6°sin(π/8 t). We set this equal to 103° to find t:

103 = 100.3 + 6sin(π/8 t)

Subtract 100.3 from both sides:

2.7 = 6sin(π/8 t)

Divide both sides by 6:

0.45 = sin(π/8 t)

We then use the inverse sine function to find values of t:

t = (8/π)sin-1(0.45)

Solving with a calculator, we get t as:

t = 1.07 days and t = 10.96 days (within the 12-day range of the illness)

Note that we take into account only the solutions within the 12-day period as only these are relevant.