Question

The function f(t) = 25 sin (pi over 2t) + 10 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?

Maximum: 35°; minimum: −15°; period: 4 hours<--- my answer
Maximum: 25°; minimum: 10°; period: pi over 2 hours
Maximum: 100°; minimum: −15°; period: pi over 2 hours
Maximum: 35°; minimum: 35°; period: 8 hours

Answer 1

The correct answer is:

Maximum: 35°; minimum: −15°; period: 4 hours

Explanation:

We are given a function f(t) which represent the temperature of a periodic chemical equation as:

`f(t)=25\sin ((\pi)/(2)t)+10`

Hence, the maximum value of the function is attained when Sine function is maximum and the minimum value is attained when the sine function attains the minimum value.

We know that the Maximum value of sine function=1

and Minimum value of Sine function is: -1

when Sine function=1

we have: f(t)=25+10=35°

Hence, Maximum value of function= 35°

Also when Sine function= -1

We have: f(t)= -25+10= -15°

Minimum value of function= -15°

Also, we know that period of sine function of the type:

`a\sin (bt)+c` is given by:

`Period=(2\pi)/(b)`

Here we have:

`b=(\pi)/(2)`

Hence,
`Period=(2\pi)/((\pi)/(2))\\\\\\Period=4`

Hence, Period=4

Answer 2

Maximum of this function: for: sin x = 1 ( maximum sin value):
25 * 1 + 10 = 25 + 10 = 35°
Minimum of this function: for sin x = -1 ( minimum sin value):
25*(-1)+10 = -25+10= -15°
Period: T=
`(2 \pi )/(b) = (2 \pi )/( ( \pi )/(2) ) = 2 * 2 = 4`
So your answer is correct: A)