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Chepi is an ecologist who studies the change in the narwhal population of the Arctic ocean over time. She


observed that the population loses 5.6% of its size every 2.8 months. The population of narwhals can be


modeled by a function, N, which depends on the amount of time, t (in months).


When Chepi began the study, she observed that there were 89,000 narwhals in the Arctic ocean.


Write a function that models the population of the narwhals t months since the beginning of Chepi's study.

Respuesta :

Answer:

[tex]P(t)=89000(0.944)^{t/2.8}[/tex]

Step-by-step explanation:

Since the population decreases by a constant factor, the growth will be modeled by an exponential decay function.

The population at time t will be:

[tex]P(t)=P_0(1-r)^{(t/k)}$ where:\\Initial Population, P_0=89,000\\$Decay Factor, r=5.6\%=0.056\\Period, k=2.8 Months\\Time in months =t[/tex]

Substituting these values, we have:

[tex]P(t)=89,000(1-0.056)^{t/2.8}\\P(t)=89000(0.944)^{t/2.8}[/tex]

Therefore, a function that models the population of the narwhals t months since the beginning of Chepi's study is:

[tex]P(t)=89000(0.944)^{t/2.8}[/tex]

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