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?

The cosine function that models this reaction is:

Step-by-step explanation:

The general cosine function has the following form

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.

is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum temperature is 160 and the minimum is 20. Then the amplitude A is:

The reaction completes a cycle in 8 hours

Then the period is 8 hours.

Thus:

The function is:

when y is minumum therefore

So

Now we substitute in the function and solve for k

Finally