quastion A Cepheid variable star is a star whose brightness alternately increase
ID: 2846168 • Letter: Q
Question
quastion
A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose that Cephei Joe is a star for which the interval between times of maximum brightness is 6.2 days. Its average brightness is 4 and the brightness changes by +/-0.2. 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) = 4 + 0.2sin(2pit/6.2) Find the rate of change of the brightness after t days. Rate of change = Find, correct to two decimal places, the rate of increase after one day. Rate of increase =Explanation / Answer
a)To find the rate of change you need to take the derivative of the function. B'(t)= .2cos(2*pie*t/6.2) * 2*pie/6.2
b)Now do B'(1) to find the rate increase per day:
.2cos(2*pie(1)/6.2)*2*pie/6.2 = 0.1264
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