AP Pre-Calculus FRQ Practice

📈AP Pre-Calculus

Guided Practice

Practice FRQ 1 of 21/2

1. The following functions are defined for this question:

p(t) = \frac{120t + 240}{t^2 + 4}

A marine biologist is studying the population of a certain species of fish in a lake. The population, in thousands of fish, can be modeled by the function

P(t) = \frac{120t + 240}{t^2 + 4}

, where

t

is the number of years since the study began, for

0 ≤ t ≤ 10

. The rate of change of the population is given by

P'(t)

$p(t) = \frac{120t + 240}{t^2 + 4}$

A. Find

P(3)

. Using correct units, explain the meaning of your answer in the context of the problem.

B. Find the average rate of change of

P(t)

over the interval

2 ≤ t ≤ 6

. Using correct units, interpret the meaning of your answer in the context of the problem.

C. Determine the end behavior of

P(t)

t

increases without bound. Express your answer using the mathematical notation of a limit, and explain what this means in the context of the fish population.