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On the first day of spring, an entire field of flowering trees blossoms. The population of locusts consuming these flowers rapidly increases as the trees blossom. The locust population gains $87 \%$ of its size every $2$.$4$ days, and can be modeled by a function, $L$, which depends on the amount of time, $t$ (in days).$\newline$Before the first day of spring, there were $1100$ locusts in the population.$\newline$Write a function that models the locust population $t$ days since the first day of spring.$\newline$$$L(t)=$$