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?
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

PLEASE HELP

Answer 1

Answer:

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

Step-by-step explanation:

The function modelling the temperature with respect to time is,

$f(t)=33\sin (\frac{\pi}{2}t)-20$

It is required to find the maximum and minimum value of the temperature.

Since, we know,

$-1\leq \sin x\leq 1$ for all values of x.

Then, $-1\leq \sin (\frac{\pi}{2}t)\leq 1$ for all values of t.

Thus, we get,

Maximum value is obtained when  $\sin (\frac{\pi}{2}t)=1$

That is, $\sin (\frac{\pi}{2}t)=1$, $f(t)=33-20=13$.

So, maximum temperature is 13°

Minimum value is obtained when  $\sin (\frac{\pi}{2}t)=-1$

That is, $\sin (\frac{\pi}{2}t)=1$, $f(t)=-33-20=-53$.

So, minimum temperature is -53°

Also, we have,

If the function f(x) has period P, then the function f(bx) will have period $\frac{P}{|b|}$.

Since, $\sin x$ has period $2\pi$, then the given function have period $\frac{2\pi }{\frac{\pi}{2}}$ = 4.

So, entire cycle takes 4 hours.

Thus, option C is correct.

Answer 2

Maximum is when  pi / 2t = 1   so that's  33-20 = 13 degrees
minimum when pi/2t = -1   - that gives -33-20 = -53 degrees

Its C