Question

He temperature of a chemical reaction ranges between 30 degrees Celsius and 70 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 10-hour period. What is a cosine function that models this reaction?

f(t) = 20 cos 10t + 50
f(t) = 50 cos 10t + 20
f(t) = −50 cos pi over 5 t + 20
f(t) = −20 cos pi over 5 t + 50

Answer 1

`f(t)=-20\cos\left((\pi)/(5)t\right)+50\\f'(t)=20\sin((\pi)/(5)t)*((\pi)/(5))=0\\\sin((\pi)/(5)t)=0\\(\pi)/(5)t=0,\pi\\t=0,5\\\\f(0)=-20\cos((\pi)/(5)(0))+50\\f(0)=-20+50\\f(0)=30\\f(5)=-20\cos((\pi)/(5)(5))+50\\f(5)=-20(-1)+50\\f(5)=20+50\\f(5)=70`

f(t) = -20 * cos(pi / 5) + 50