Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She observed that the populati
on decays by a factor of 8/9 every 4 months. The population of penguins can be modeled by a function, P, which depends on the amount of time, t (in months). When Talulah began the study, she observed that there were 27,000 penguins in Antarctica. Write a function that models the population of the penguins t months since the beginning of Talulah's study. P(t) =
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Answer:
Step-by-step explanation:
The function that could model this periodic phenomenon will be of the form
The tide varies between 3ft and 9ft, which means its amplitude is
and its midline is
.
Furthermore, since at the tide is at its lowest ( 3 feet ), we know that the trigonometric function we must use is
.
The period of the full cycle is 14 hours, which means
giving us
With all of the values of the variables in place, the function modeling the situation now becomes