The function f(t) = 20 sin (pi over 5t) + 12 models the temperature of a periodic chemical reaction where t represents time in hours. what are the maximum and minimum temperatures of the reaction, and how long does the entire cycle take? a. maximum: 20°; minimum: 8°; period: 12 hours b. maximum: 32°; minimum: −8°; period: 10 hours c. maximum: 20°; minimum: 12°; period: pi over 5 hours d. maximum: 32°; minimum: 8°; period: pi over 5 hours

option B. Maximum: 32°; minimum: −8°; period: 10 hours

Explanation:

1) Given function:

f(t) = 20 sin (π/5 t) + 12

2) Maximum

The maximum value of the sine function is 1. Therefore, the maxmum of f(t) is 20 (1) + 12  = 20 + 12 = 32

3) Minimum

The minimum value of the sine function is - 1. Therefore, the minimum of f(t) is 20 (-1) + 12  = - 20 + 12 = - 8

4) How long does the entire cycle take?


The cycle of the function sine is 2π.

That means that the value of sine (x) repeats each time that x is a multiple of 2π.

The first cycle of 20 sin(π/5t) is from π/5 t = 0 to π/5 t = 2π

π/5 t = 0 ⇒ t = 0, π/5 t = 2π ⇒ t = 10.

So, every cycle is of 10 hours.

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