(Solved): A Cepheid variable star is a star whose brightness alternately increases and decreases. Suppose tha ...

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 4.1 days. Its average brightness is 2.8 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 $i$ days: $B(t)=2.8+0.2\sin (2?t/4.1)$ (a) Find the rate of change of the brightness after $t$ days. Rate of change $=$ (b) Find the rate of increase after one day. Rate of increase $=$