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 5.1 days. Its average brightness is 3.6 and the brightness changes by +/-0.55. 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)=3.6+0.55sin(2pi(t)/5.1)

I found the rate of change.. it's
0.677598cos(1.232t)

But, I also need to find the rate of increase after one day. (correct to two decimal places)

can someone help?

Question

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 5.1 days. Its average brightness is 3.6 and the brightness changes by +/-0.55. 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)=3.6+0.55sin(2pi(t)/5.1)

I found the rate of change.. it's
0.677598cos(1.232t)

But, I also need to find the rate of increase after one day. (correct to two decimal places)

can someone help?

anonymous · Answer

To find the rate of increase after one day,
Substitute t=1 in B(t)=3.6+0.55sin(2pi(t)/5.1)
=> B(1) = 3.6+0.55sin(2pi/5.1)
Simplify this to find the answer.