Will medal and fan for anyone one who helps me

Question

princesskitty01 · Answer

The temperature of a chemical reaction ranges between 20 degrees Celsius and 160 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during an 8-hour period. What is a cosine function that models this reaction?

 f(t) = −90 cos (pi over 4t) + 70
 f(t) = −70 cos (pi over 4t) + 90
 f(t) = 70 cos (8t) + 90
 f(t) = 90 cos (8t) + 70

princesskitty01 · Answer

i think B sorry was doing the others

campbell_st · Answer

well start by looking at the period of the curve

you know the period is 8 hours 

and in a cos function 

$$y = acos(bx) $$

the period is 

$$period = \frac{2\pi}{b}$$

so then using the given information 

$$8 = \frac{2\pi}{b}$$

solve for b... 

when you find b you will eliminate 2 answer choices

then work on the amplitude and phase shift

princesskitty01 · Answer

okay

campbell_st · Answer

next find the amplitude of the curve if it has a minimum of 20 and max of 160 the coss curve is centered between those values... 

so to find centre add the 2 limit values and divide by 2, that will give the value of a in 

$$y = acos(bx)$$

princesskitty01 · Answer

okay

campbell_st · Answer

can you check your 1st 2 answer choices 

are they -90 and -70     or should they be 90 and 70..?

princesskitty01 · Answer

thx