#### Problem 77E

77. A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei, for which the interval between times of maximum brightness is $5.4$ days. The average brightness of this star is $4.0$ and its brightness changes by $\pm 0.35 .$ In view of these data, the brightness of Delta Cephei at time $t$, where is measured in days, has been modeled by the function

$$B(t)=4.0+0.35 \sin \left(\frac{2 \pi t}{5.4}\right)$$

(a) Find the rate of change of the brightness after $t$ days.

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