## vera_ewing one year ago The temperature of a chemical reaction ranges between 30°C and 70°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?

1. vera_ewing

@Michele_Laino f(t) = 50 sin 10t + 20 ?

2. Michele_Laino

the amplitude of your function, is: $\Large A = \frac{{\max value - \min value}}{2} = \frac{{70 - 30}}{2} = ...?$

3. vera_ewing

40/2 = 20

4. vera_ewing

f(t) = 20 sin 10t + 50 is the answer?

5. Michele_Laino

we can write: $\Large f\left( t \right) = 20\sin \left( {Bt} \right) + 50$ since we have these limit values: $\Large 30 \leqslant 20\sin \left( {Bt} \right) + 50 \leqslant 70$

6. Michele_Laino

now we have to determine the value of the constant B

7. vera_ewing

So it's f(t) = 20 sin pi/5 t + 50 ?

8. Michele_Laino

I think that we have: $\Large B = \frac{{2\pi }}{6}$ since our function has to assume the same values after 6 hours

9. Michele_Laino

therefore: $\Large f\left( t \right) = 20\sin \left( {\frac{{2\pi }}{6}t} \right) + 50$ is the right function

10. vera_ewing

11. vera_ewing

Those are my answer choices ^

12. Michele_Laino

please wait a moment, I'm pondering...

13. Michele_Laino

14. Michele_Laino

maybe there is a typo since we can rewrite our function as below: $\Large f\left( t \right) = 20\sin \left( {\frac{\pi }{3}t} \right) + 50$

15. Michele_Laino

please wait a moment, I understand

16. Michele_Laino

17. vera_ewing

So which one should I choose?

18. Michele_Laino

try with the last option, please

19. Michele_Laino

is the period T=10 hours?

20. Michele_Laino

I think that there is a typo, namely: T=10 hours and not T=6 hours