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Problem 81 Hard Difficulty

A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cephei, for which the interval between times of maximum brightness is 5.4 days. The average brightness of this star is 4.0 and its brightness changes by $ \pm O.35. $ In view of these data, the brightness of Delta Cephei at time $ t, $ where $ t $ is measured in days, has been modeled by the function
$ B(t) = 4.0 + 0.35 \sin (\frac {2 \pi t}{5.4}) $
(a) Find the rate of change of the brightness after $ t $ days.
(b) Find, correct to two decimal places, the rate of increase alter one day.

Answer

a. $\frac{7 \pi}{54} \cos \left(\frac{2 \pi t}{5.4}\right)$
b. Rate of increase after one day is 0.161

Discussion

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FE

Francis E.

September 9, 2020

Video Transcript

the brightness of the star after two days is given as the A. T. 4.0 plus 0.357 to 5 to year over. 5.4. Give us information. We want to answer A and B. Find the rate of change and be after two days and be fined the rate of change of the after one day. As a note at the top indicates, this question is showing the understanding of different information using the channel. That is G. F. G. X. Dx is equal to F. Prime G of X. Where there were a half with G plugged in candy product. So to find the rate of change of B. After two days using the chamber, we have been trying to 40 or four plus 40.359 to 5 to 5.4 point 35 times signed. 2.25 point four G of X. Being to 5 to 5.4 G. Has delivered into five or 5.4. That's our Salvation 0.755 point 4% to 5 to 1.54 and B. We find the rate of change up to one day, such as two years and days. You simply plug in one. Thus, we find one is 10.75 or 5.4% to 5 times 1/5 50.4. Using a calculator, we obtain 0.16 per day for changing brightness per day.