Question

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.

Answer 1

`P(t)=89000(0.944)^(t/2.8)`

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:

`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`

Substituting these values, we have:

`P(t)=89,000(1-0.056)^(t/2.8)\\P(t)=89000(0.944)^(t/2.8)`

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

`P(t)=89000(0.944)^(t/2.8)`