Question

The pressure P (in lbs/ft2), in a pipe varies overtime. Five times an hour, the pressure oscillates from a lowof 90 to a high of 230 and then back to a low 90. Thepressure at t = 10 is 90. a) Graph P = f(t), where t is time in minutes. b) Find a possible formula for P = f(t). c) By graphing P = f(t) for 0 t 2, estimate when the pressure first equals115 lbs/ft2. d)what is the pressure at 23 minutes?

Answer 1

Answer :

Since the function starts at an extreme, it is convenient to use the cosine function, which is at an extreme when its argument is zero. The cosine function has extremes of ±1 from its average value of 0. So, you need to translate and scale it to match the problem.

The average value of the pressure is (90 +230)/2 = 160. The starting extreme is 90 -160 = -70. This means your cosine function will look like
.. f(t) = 160 -70cos( )
“5 times per hour” means the period is 12 minutes. If we use t in minutes (not hours), then when t changes by 12, the argument of the cosine function changes by 2π. We can write that argument as (2πt)/12 = πt/6. We’re done.

b) f(t) = 160 -70cos(πt/6)