A few weeks into the SARS $($severe acute respiratory syndrome$)$ epidemic in $2003,$ the number of cases was increasing by about $4\%$ each day. $$ On April $1,2003,$ there were $1,804$ cases. Find an exponential model that predicts the number of cases $t$ days after April $1,2003.$

$f(t)=$

$$

Use it to estimate the number of cases on April $30,2003.($Round your answer to the nearest integer. The actual reported number of cases was $5,663.)$

$$ cases