anonymous
  • anonymous
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
Mathematics
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anonymous
  • anonymous
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
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
anonymous
  • anonymous
anonymous
  • anonymous

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Michele_Laino
  • Michele_Laino
the amplitude A of your function is: \[\Large A = \frac{{180 - 40}}{2} = ...?\]
anonymous
  • anonymous
140/2= 70
anonymous
  • anonymous
So A?
Michele_Laino
  • Michele_Laino
no, since the period of our function is 12 hours, so the shape og our function has to be this: \[\Large \cos \left( {\frac{{2\pi }}{{12}}t} \right)\]
Michele_Laino
  • Michele_Laino
of*
anonymous
  • anonymous
It's really hard so I don't really know what to plug in for the shape of function
Michele_Laino
  • Michele_Laino
since at t=0, the value is 40, then we have this drawing: |dw:1436896425801:dw|
Michele_Laino
  • 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
anonymous
  • anonymous
Oh okay so what is next? @Michele_Laino
Michele_Laino
  • Michele_Laino
please substitute t=0 into the third option, what do you get? f(0)=...?
anonymous
  • anonymous
-70 cos + 110?
anonymous
  • anonymous
Michele_Laino
  • Michele_Laino
we have: \[\Large - 70\left( {\cos 0} \right) + 110 = - 70 \times 1 + 110 = 40\]
Michele_Laino
  • Michele_Laino
so, what can you conclude?
anonymous
  • anonymous
I can conclude the answer is C.
Michele_Laino
  • Michele_Laino
that's right!
anonymous
  • anonymous
Yay.
Michele_Laino
  • Michele_Laino
:)

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