Values of a function are given in the following table. Explain why this function

Question

Values of a function are given in the following table. Explain why this function appears to be periodic. Approximately what are the period and amplitude of the function? Assuming that the function is periodic, estimate its value at 10, at t 65 and at 130 20 25 30 35 40 45 50 55 60 f (t) 1.8 1.4 1.7 2.3 2.0 1.8 1.4 1.7 2.3 Enter the exact answers. The function appears to be periodic because the table data begins to repeat itself at The period is The amplitude is mnrmrmrmrmrmnrm,rmrmrmrmrrm,F. f (10) f (65

Explanation / Answer

A periodic function is one which returns to the same value at regular intervals.

a). As we can see that the value of the function returns to the same value, that is,

when t=20,f(t)=1.8 and then again at t=45,f(t)=1.8,

So, the function appears to be periodic because the table data begins to repeat itself at t = 45

b). Period of a function is the value of t after which the function starts returning to the same value.

Like in this case, the function starts returning to the same value after t = 45 - 20 = 25

So, the period is 25.

c). Amplitude is the value from the mean value of the function to it's maximum or minimum value.

So,here amplitude = (Max. value - Min. value)/2 = (2.3-1.4)/2 = 0.45

d). Since the function is periodic,

we have, f(20) = 1.8

f(15) = 2.0

  f(10) = 2.3

e). Similarly,

f(60) = 2.3

  f(65) = 2.0

  

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