Limited population growth: Human Population. Seventeen adults came ashore from the British ship HMS Bounty in 1970 to settle on the uninhabited South Pacific Island Pitcairn. The population, P ( t ) , of the island t years after 1790 can be approximated by the logistic equation P ( t ) = 3400 17 + 183 e − 0.982 t ( Source : www.government.pn) a. Find the population of the Island after 10 yr, 50 yr, and 75 yr. b. Find the rate of change in the population, P ' ( t ) . c. Find the rate of change in the population after 10 yr, 50 yr, and 75 yr. d. What is the limiting value for the population of Pitcairn? (The limiting value is the number to which the population gets closer and closer but never reaches.)
Limited population growth: Human Population. Seventeen adults came ashore from the British ship HMS Bounty in 1970 to settle on the uninhabited South Pacific Island Pitcairn. The population, P ( t ) , of the island t years after 1790 can be approximated by the logistic equation P ( t ) = 3400 17 + 183 e − 0.982 t ( Source : www.government.pn) a. Find the population of the Island after 10 yr, 50 yr, and 75 yr. b. Find the rate of change in the population, P ' ( t ) . c. Find the rate of change in the population after 10 yr, 50 yr, and 75 yr. d. What is the limiting value for the population of Pitcairn? (The limiting value is the number to which the population gets closer and closer but never reaches.)
Solution Summary: The author explains how to calculate the population of the island Pitcairn after 10yr. The formula is P(t)=340017+
Limited population growth: Human Population. Seventeen adults came ashore from the British ship HMS Bounty in 1970 to settle on the uninhabited South Pacific Island Pitcairn. The population,
P
(
t
)
,
of the island t years after 1790 can be approximated by the logistic equation
P
(
t
)
=
3400
17
+
183
e
−
0.982
t
(Source: www.government.pn)
a. Find the population of the Island after 10 yr, 50 yr, and 75 yr.
b. Find the rate of change in the population,
P
'
(
t
)
.
c. Find the rate of change in the population after 10 yr, 50 yr, and 75 yr.
d. What is the limiting value for the population of Pitcairn? (The limiting value is the number to which the population gets closer and closer but never reaches.)
University Calculus: Early Transcendentals (4th Edition)
Precalculus Enhanced with Graphing Utilities
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY