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 5.3 days. Its average brightness is 2.9 and the brightness changes by /- 0.35. 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)=4.2 +0.45sin(2pit/4.4) (a) Find the rate of change of the brightness after t days.
(b) Find the rate of increase after one day.