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?
Maximum: 20°; minimum: 8°; period: 12 hours
Maximum: 32°; minimum: −8°; period: 10 hours
Maximum: 20°; minimum: 12°; period: pi over 5 hours
Maximum: 32°; minimum: 8°; period: pi over 5 hours
The answer for the exercise shown above is the second option, which is: Maximum: 32°; minimum: −8°; period: 10 hours. The explanation is shown below: You can make a graph of the function given in the problem above: f(t)=20Sin(π/5t)+12. As you can see in the graph, the maximum point is at 32 over the y-axis, and the minimum is at -8. The lenght of the repeating pattern of the function (Its period) is 10.
