Question

The population in millions of arctic flounder (a type of fish) in the Atlantic Ocean is modeled by the function p(t) = 9t² - 168t + 0.4123, where t is measured in years. What is the population of arctic flounder in the Atlantic Ocean after 5 years?

1) 0.4123 million
2) 1.4123 million
3) 2.4123 million
4) 3.4123 million

Answer 1

The population model predicts the arctic flounder population in the Atlantic Ocean after 5 years would be 0.4123 million; however, the negative value after calculations suggests extinction, making 0.4123 million the closest possible answer given.

Step-by-step explanation:

The student is asking for the population of arctic flounder in the Atlantic Ocean after 5 years using a given mathematical model. The function presented is p(t) = 9t² - 168t + 0.4123, where t represents the time in years, and p(t) represents the population in millions. To calculate the population after 5 years, we simply substitute t with 5:

p(5) = 9(5)² - 168(5) + 0.4123

= 9(25) - 840 + 0.4123

= 225 - 840 + 0.4123

= -615 + 0.4123

= -614.5877 million

Since a negative population is not possible, this indicates that the model predicts the population of arctic flounder will be essentially extinct after 5 years. Therefore, the population would be most closely represented by the first answer choice:

1) 0.4123 million