Modeling Narwhal Population Dynamics

Cheppy, an ecologist, studies the narwhal population in the Arctic Ocean, observing a 5.6% decrease every 2.8 months. The population is modeled by an exponential function, starting with 89,000 narwhals. The video explains how to create this function, using a table to understand the population's behavior over time. The function is based on the initial population and the common ratio of 0.944, representing the population's retention rate every 2.8 months. The video concludes with a complete model of the narwhal population.

What was the initial population of narwhals observed by Cheppy in the Arctic Ocean?

• 95,000

• 89,000

• 75,000

• 100,000

How much does the narwhal population decrease every 2.8 months?

• 10%

• 7%

• 5.6%

• 3.5%

What is the percentage of the population retained after a 5.6% decrease?

• 92.5%

• 95%

• 90%

• 94.4%

What mathematical concept is used to model the narwhal population decrease over time?

• Quadratic growth

• Exponential decay

• Logarithmic decay

• Linear decay

What is the common ratio used in the exponential function for the narwhal population?

• 0.856

• 0.980

• 0.944

• 0.900

How is the number of 2.8-month periods calculated in the function?

• By multiplying the months by 2.8

• By dividing the months by 2.8

• By adding 2.8 to the months

• By subtracting 2.8 from the months

What happens to the function when t equals zero?

• The function equals infinity

• The function equals the common ratio

• The function equals the initial population

• The function equals zero

What is the exponent in the function when t is 5.6 months?

• 0

• 1

• 3

• 2

What is the purpose of graphing the function or using a calculator as suggested in the video?

• To verify the function's accuracy

• To find the initial population

• To determine the common ratio

• To calculate the percentage decrease

What is the final step in modeling the narwhal population according to the video?

• Determine the common ratio

• Graph the function

• Calculate the initial population

• Underline the function