(Solved): A Cepheid variable star is a star whose brightness alternately increases and ...

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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 \( 6.6 \) days. Its average brightness is \( 3.8 \) and the brightness changes by \( +/-0.6 \). Using this data, we can construct a mathematical model for the brightness of Cephei Joe at time \( t \), where \( t \) is measured in days: \[ B(t)=3.8+0.6 \sin (2 \pi t / 6.6) \] (a) Find the rate of change of the brightness after \( t \) days. Rate of change \( = \) (b) Find the rate of increase after one day.