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

Answer:

0.41 (correct to 2 decimal place)

Step-by-step explanation:

If $B(t)=4.0+0.35sin\frac{2\pi t }{5.4}$

Let $u=\frac{2\pi t }{5.4}$, then $B(u)=4.0+0.35sin u$

We want to determine the rate of increase $\frac{dB}{dt}$ after one day

$du=\frac{2\pi dt }{5.4}$ and $\frac{dB}{du} =0.35cos u$

$\frac{dB}{dt}=\frac{2\pi }{5.4}0.35cos (\frac{2\pi t }{5.4})=0.407cos (\frac{2\pi t }{5.4})$

$B^{'} (t)=0.407cos (\frac{2\pi t }{5.4})$

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

$B^{'} (1)=0.407cos (\frac{2\pi X 1 }{5.4})$= 0.407 =0.41 (correct to 2 decimal place)