Question

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period. What is a cosine function that models this reaction?
f(t) = −30 cos (pi/3) t + 20

f(t) = −60 cos (pi/3) t + 30

f(t) = 30 cos (6t) + 20

f(t) = 60 cos (6t) + 30

Answer 1

maximum amount of cos is 1 and it's minimum is -1 so the answer should be something you put 1 and -1 (without attaining to cos itself) find -10 and 50
so it's the first one or the third one
(period)T=2pi/a
6=2pi/a
a=pi/3
the first one is the answer

Answer 2

Answer:

Option 1 - $f(t)=-30 sin(\frac{\pi}{3}t)+20$

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

Solution :

General form of cosine function is $f(x)=A cos(Bx)+C$

Where A is the amplitude

$B=\frac{2\pi}{\text{Period}}$

C is the midline    

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e, $A=\frac{-10-50}{2}=-30$

Period of 1 cycle is 6 hour

So, $B=\frac{2\pi}{6}=\frac{\pi}{3}$

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So, $f(t)=A\cos t+C$

$-10=-30\cos 0+C$

$C=20$

Substituting the values we get,

The cosine function is  $f(t)=-30 sin(\frac{\pi}{3}t)+20$

Therefore, Option 1 is correct.