A variable star is one whose brightness alternately increases and decreases. For one such star, the time between periods of maximum brightness is$5\mathrm{.}2$days$,$the average brightness $($or magnitude$)$ of the star is$5\mathrm{.}1,$ and its brightness varies by$0\mathrm{.}40$magnitude$.$ Find a function that models the brightness of the star as a function of time $($in days$),$t$.($Assume that at$$

t$=0$

$$the brightness of the star is$5\mathrm{.}1$and that the function is increasing.$)$

f$($t$)=$

$$