A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservation measures are implemented, it is hoped that the turtle population will grow according to the rule , where N(t) denotes the population at the end of year t. Find the rate of growth of the turtle population when .
A) 26 turtles/yr
B) 28 turtles/yr
C) 24 turtles/yr
D) 30 turtles/yr
E) 32 turtles/yr

Question

A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservation measures are implemented, it is hoped that the turtle population will grow according to the rule  , where N(t) denotes the population at the end of year t. Find the rate of growth of the turtle population when  .
A) 26 turtles/yr 
B) 28 turtles/yr 
C) 24 turtles/yr 
D) 30 turtles/yr 
E) 32 turtles/yr

Quizplus · Accepted Answer

We are given that the population growth of the turtles follows the rule:

N(t) = 5000(1 + 0.06)^t

To find the rate of growth of the population, we need to find the derivative of N(t):

dN/dt = 5000(0.06)(1 + 0.06)^(t-1)

At t = 5, we have:

dN/dt = 5000(0.06)(1 + 0.06)^(5-1) = 30

Therefore, the rate of growth of the turtle population at the end of 5 years is 30 turtles per year.

The correct answer is (D) 30 turtles/yr.

A Certain Species of Turtle Faces Extinction Because Dealers Collect