Question

The function f(t) = 33 sin (pi over 2t) − 20 models the temperature of a periodic chemical reaction where t represents time in hours. What are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take? (5 points)

Maximum: 53°; minimum: −13°; period: 4 hours

Maximum: 33°; minimum: 20°; period: pi over 2 hours

Maximum: 13°; minimum: −53°; period: 4 hours

Maximum: 35°; minimum: 35°; period: 8 hours

Answer 1

The given function is

`f(t) = 33 sin( ( \pi )/(2) t) - 20`
with
t = time, hours
f = temperature, °C


Because the maximum and minimum values for the Sine function are +1 and -1 respectively,
The maximum value of f = 33 - 20 = 13.
The minimum value of f = -33 - 20 = -53.

The period, T, is given by

`(2 \pi )/(T) = ( \pi )/(2) \\ \\ T=4`

Answer:
Maximum: 13°; Minimum: -53°; period: 4 hours