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 6.2 days. The average brightness of this star is 3.0 and its brightness changes by ±0.25. 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)=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.

a)

b) 0.09

Step-by-step explanation:

We are given the following in the question:

where B(t) gives the brightness of the star at time t, where t is measured in days.

a) rate of change of the brightness after t days.

b) rate of increase after one day.

We put t = 1

The rate of increase after 1 day is 0.09

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363