## anonymous one year ago The temperature of a chemical reaction ranges between 40 degrees Celsius and 180 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 12-hour period. What is a cosine function that models this reaction? f(t) = 70 cos 12t + 110 f(t) = 110 cos 12t + 70 f(t) = −70 cos pi over 6t + 110 f(t) = −110 cos pi over 6t + 70

1. anonymous

@Jacob902 @pooja195 @Hero

2. anonymous

@ganeshie8

3. anonymous

@Michele_Laino @dan815

4. Michele_Laino

the amplitude A of your function is: $\Large A = \frac{{180 - 40}}{2} = ...?$

5. anonymous

140/2= 70

6. anonymous

So A?

7. Michele_Laino

no, since the period of our function is 12 hours, so the shape og our function has to be this: $\Large \cos \left( {\frac{{2\pi }}{{12}}t} \right)$

8. Michele_Laino

of*

9. anonymous

It's really hard so I don't really know what to plug in for the shape of function

10. Michele_Laino

since at t=0, the value is 40, then we have this drawing: |dw:1436896425801:dw|

11. Michele_Laino

now, if I set t=0 into the first option I get: f(0)= 180 so the first option is not the right option

12. anonymous

Oh okay so what is next? @Michele_Laino

13. Michele_Laino

please substitute t=0 into the third option, what do you get? f(0)=...?

14. anonymous

-70 cos + 110?

15. anonymous

@Michele_Laino

16. Michele_Laino

we have: $\Large - 70\left( {\cos 0} \right) + 110 = - 70 \times 1 + 110 = 40$

17. Michele_Laino

so, what can you conclude?

18. anonymous

I can conclude the answer is C.

19. Michele_Laino

that's right!

20. anonymous

Yay.

21. Michele_Laino

:)