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 of maximum brightness is 5.7 days. The average brightness of this star is 2.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function

B(t) = 2.0 + 0.25 sin (2t/ 5.7) .

(a) Find the rate of change of the brightness after t days. dB/ dt =

(b) Find, correct to two decimal places, the rate of increase after one day. dB /dt =

Explanation / Answer

Solution:

B(t) = 2.0 + 0.25 sin (2t/ 5.7)

(a)

rate of change of the brightness after t days. dB/ dt = 0.25*(2/ 5.7)* cos (2t/ 5.7)

(b)

the rate of increase after one day. dB /dt =

t = 1, then we obtain B'(1) = 0.25*(2/ 5.7) * cos (2t/ 5.7)

B'(1) 0.1244

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