A Cepheid variable star is a star whose brightness alternately increases and dec

Question

A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times or maximum brightness is 4.1 days. The average brightness of this star is 3.0 and its brightness changes by plus minus 55. In view of these data, the brightness of the star at time t, where r Is measured in days, has been modeled by the function B(t) = 3.0 + 0.55 sln (2 pi t/4.1). Find the rate of change of the brightness after t days. dB/dt = Find, correct to two decimal places, the rate of increase after four days. dB/dt =

Explanation / Answer

a)
B(t) = 3.0 + 0.55 sin (2*pi*t/4.1)
dB/dt = d/dt (3.0) + d/dt (0.55 sin (2*pi*t/4.1))
dB/dt = 0 + 0.55*2*pi/4.1 cos (2*pi*t/4.1)
            = 0.27pi* cos (2*pi*t/4.1)
            = 0.85* cos (2*pi*t/4.1)

b)
at t= 4
dB/dt= 0.85* cos (2*pi*t/4.1)
           = 0.85* cos (2*pi*4/4.1)
           = 0.85 * cos (6.13 rad)
           = 0.85 * 0.988
           = 0.84
Answer: 0.84

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