math prob in des.

Question

The temperature of a chemical reaction ranges between –10°C and 50°C. The temperature is at its lowest point when t = 0 and completes one cycle over a six-hour period. What is a sine function that would model this reaction?

Answer 1

Lowers point -10 & highest point 50

So,amplitude= 30

 

Period is  6 hours

 

asin(bx+c)+d.    general function

 

2pi/b =6

b= pi/3

 

Lowest point  t=0   at value  -10

 

Total period/4= 6/4=3/2=1.5

 

So, 

 

c/b =1.5

c*3/pi= 1.5

 

c= 0.5*pi

 

d = 20

 

So,

 

30sin(pi*x/3.  -0.5*pi)+20

 

is the final sin function