Question

The temperature of a chemical reaction oscillates in the interval 44 °C to 50 °C. The temperature is at 47 °C at t = 0 and rises at the start of a four-minute cycle. Which function represents the relationship between time, t, and temperature, T?

Answer 1

T= 47 + 3 * sin (t
`\pi`/2)

Explanation:

To make oscillates function you need to use sin/cos function, based on if the function increase or decreases first. This function rises at the start so it uses sin function. The function will look like this .

T= sin (t 2
`\pi`)

The temperature starts at 47. Then the function changes into

T= 47 + sin (t 2
`\pi`)

The temperature peak at 50 and the lowest at 44. Basically it's 47 +/- 3. It also has a 4-minute cycle, so the frequency is 1/4. Then the final function will be:

T= 47 + 3 * sin (t 2
`\pi`/4)

T= 47 + 3 * sin (t
`\pi`/2)