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 3.8 days. The average brightness of this star is 2.0 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

Answer 1

0.41 (correct to 2 decimal place)

Explanation:

If
`B(t)=4.0+0.35sin(2\pi t )/(5.4)`

Let
`u=(2\pi t )/(5.4)`, then
`B(u)=4.0+0.35sin u`

We want to determine the rate of increase
`(dB)/(dt)` after one day

`du=(2\pi dt )/(5.4)` and
`(dB)/(du) =0.35cos u`

`(dB)/(dt)=(2\pi )/(5.4)0.35cos ((2\pi t )/(5.4))=0.407cos ((2\pi t )/(5.4))`

`B^(') (t)=0.407cos ((2\pi t )/(5.4))`

Rate of increase after one day, i.e. t=1

`B^(') (1)=0.407cos ((2\pi X 1 )/(5.4))`= 0.407 =0.41 (correct to 2 decimal place)