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? (5 points)

A. Maximum: 25°; minimum: 10°; period: pi over 2 hours
B. Maximum: 35°; minimum: 35°; period: 8 hours
C. Maximum: 100°; minimum: −15°; period: pi over 2 hours
D. Maximum: 35°; minimum: −15°; period: 4 hours

Answer 1

The correct answer is: Option: D

D. Maximum: 35° ; minimum: −15° ; Period: 4 hours

Explanation:

We are given a function f(t) as:

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

We know that the maximum value of the function is obtained when the sine function is maximum.

i.e. when sine takes the value=1

and the minimum value of the function is obtained when the sine function is minimum.

i.e. when sine takes the value= -1

Hence, the minimum value of the function is:

-25+10= -15

and the maximum value of the function is:

25+10=35

Also the period of the function of the type:

`f(x)=a\sin(bx)+c`

is:

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

Hence, here we have: b=π/2

Hence, period is:

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

Hence, option: D is the correct answer.

Answer 2

f(t) = 25 sin [(π/2) t] + 10

By graphing the given function
The correct option is D
D. Maximum: 35°; minimum: −15°; period: 4 hours