(6 points) A Cepheid variable star is a star whose brightness alternately increa
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Question
(6 points) 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 2.4 and the brightness changes by +/-0.5. 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) = 2.4 + 0.5 sin(27rt/6) (a) Find the rate of change of the brightness after t days Rate of change (b) Find the rate of increase after one day. Rate of increase =Explanation / Answer
(a) Differentiating with respect to t, we get
B'(t) = 0.5(2 /6) cos(2 t/6) = (/6) cos(2 t/6)
(b) After one day, B'(1) = (/6) cos(2 /6) = /12
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