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

Answer:

The correct answer is: Option: D

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

Step-by-step explanation:

We are given a function f(t) as:

          $f(t)=25\sin (\dfrac{\pi}{2}t)+10$

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:

$Period=\dfrac{2\pi}{b}$

Hence, here we have: b=π/2

Hence, period is:

$Period=\dfrac{2\pi}{\dfrac{\pi}{2}}\\\\\\Period=4$

         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