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. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6 days. Its average brightness is 4.1 and the brightness changes by +/-0.25. Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time t, where t is measured in days: B(t) = 4.1 + 0.25sin(27pit/6) Find the rate of change of the brightness after t days. Rate of change = 3m Find the rate of increase after one day. Rate of increase =

Explanation / Answer

Given that brightness at time t is

B(t) = 4.1 + 0.25 sin (2t/6)

a) rate of change of brightness after t days is

dB(t)/dt = 0 + 0.25 cos (2t/6) . 2/6

= (/12)  cos (2t/6)

Therefore,

rate of change = (/12)  cos (2t/6)

b) t = 1 day

rate of increase after 1 day = (/12)  cos (2.1/6)

=  (/12) . cos (/3)

= (/12) . (1/2)

= 0.13

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