Rate of Change of the Brightness

Question

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 5.1 days. The average brightness of this star is 2.0 and its brightness changes by ±0.55. 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

B(t) = 2.0 + 0.55 sin(2πt/5.1)



(a) Find the rate of change of the brightness

after t days.

dB/dt=?

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

dB/dt=?

Answer 1

Answer 2

dB/dt = 0.55 x (2π /5.1) cos (2πt/5.1)

This comes from d/dt sin (nt) = n cos (nt)

then just find dB/dt when t=1

Mike