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 days. Its average brightness is 3.5 and the brightness changes by /-0.25. 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)=4.2 +0.45sin(2pit/4.4) A) Find the rate of change of the brightness after t days.
B) Find the rate of increase after one day.

a) The rate of change of the brightness after t days is

b) The rate of increase after one day is of 0.0915.

Step-by-step explanation:

The brightness after t days is given by:

A) Find the rate of change of the brightness after t days.

This is

The derivative of a constant is 0, the derivative of is

So, in this case, we have that:

The rate of change of the brightness after t days is

B) Find the rate of increase after one day.

This is . So

The rate of increase after one day is of 0.0915.

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step-by-step explanation:

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step-by-step explanation:

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