(1 pt) A Cepheid variable star is a star whose brightness alternately increases

Question

(1 pt) 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 4.9 days. Its average brightness is 2 and the brightness changes by +/-0.6. 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) = 2 + 0.6 sin(2piet/4.9) (a) Find the rate of change of the brightness after t days. Rate of change = 0.6sin(2pit/4.9)+4.9 (b) Find the rate of increase after one day. Rate of increase = 0.6 sin(2pi*1/4.9)

Explanation / Answer

B(t)=2+0.6sin(2*pi*t/4.9)
a.) B'(t)=0.6*cos(2*pi*t/4.9)*(2*pi/4.9)
b.) B'(1)=0.6*cos(2*pi/4.9)*(2*pi/4.9)

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