Question

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?

Answer 1

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

Answer 2

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

Answer 3

40/2 = 20

Answer 4

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

Answer 5

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

Answer 6

now we have to determine the value of the constant B

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

Those are my answer choices ^

Answer 11

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

Answer 12

please look at this drawing:

Answer 13

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

Answer 14

please wait a moment, I understand

Answer 15

I confirm my answer above

Answer 16

So which one should I choose?

Answer 17

try with the last option, please

Answer 18

is the period T=10 hours?

Answer 19

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