Question

The population in millions of Arctic flounder (a type of fish) in the Atlantic Ocean is modeled by the function P(t) = 3t² - 2t + 7. Find P'(t).

Answer 1

The derivative P'(t) of the function P(t) = 3t² - 2t + 7, which models the Arctic flounder population in the Atlantic Ocean, is calculated as P'(t) = 6t - 2.

Step-by-step explanation:

To find P'(t), we need to calculate the derivative of the function representing the population in millions of Arctic flounder in the Atlantic Ocean, which is given by P(t) = 3t² - 2t + 7. The derivative of a function at any point gives us the rate of change of the function's value with respect to its variable. In this case, it would give us the rate at which the population is changing over time.

The derivative of P(t) with respect to t is calculated as follows:

• The derivative of 3t² with respect to t is 6t.
• The derivative of -2t with respect to t is -2.
• The derivative of a constant, such as 7, is 0.

Therefore, the derivative P'(t) is equal to:

P'(t) = 6t - 2