Calculus Problem, brightness of a star

Question

A Cepheid variable star is a star whose brightness, B , alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.1 days. Its average brightness is 5 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) = 5 + 0.6sin ( 2pi(t) / 6.1)

(a) Find the rate of change of the brightness, in units of brightness per day, after  t

 days.

Rate of change =

(b) Find the rate of change of increase, in units of brightness per day, after one day.

Rate of change of increase =

Answer 1

B(t)=5+0.6sin(2πt/6.1)

a)

Rate of change =

dB/dt = B'(t) = 0.6(2π/6.1)cos(2πt/6.1) = 0.1967πcos(2πt/6.1) units of brightness per day

b)

Rate of change of increase =

B'(1) = 0.1967πcos(2π/6.1) = 0.61785 units of brightness