Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She observed that the population decays by a factor of \dfrac{8}{9} 9
8

start fraction, 8, divided by, 9, end fraction every 444 months. The population of penguins can be modeled by a function, PPP, which depends on the amount of time, ttt (in months).
When Talulah began the study, she observed that there were 27{,}00027,00027, comma, 000 penguins in Antarctica.
Write a function that models the population of the penguins ttt months since the beginning of Talulah's study.
P(t) =P(t)=P, left parenthesis, t, right parenthesis, equals