A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 4.9 days. The average brightness of this star is 4.0 and its brightness changes by ±0.35. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function 2(pi)t. B(t) = 4.0 + 0.35sin(- 4.9/
(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.