My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
April 18th, 2010, 04:15 AM   #1
Joined: Apr 2010

Posts: 91
Thanks: 0

Derivatives/linear approximation problem

The population of a certain country grew from 2.1 million in 1970 to 3 million in 1995.

a) What was the average rate of change of the population over that period? (worked out to be 36 thousand people per year).

b)Suppose that the population grew exponentially. By what percentage did the population grow each year? What was the average rate of change from 1970 to 1975? What was the average rate of change from 1990 to 1995? Illustrate your answers using a sketch.

I worked out no. a), but I am having problems with number b) could some please help? This question appeared under a section in my note under the heading of derivatives and linear approximations, so I am thinking you have to use that to solve the problem.
TsAmE is offline  
April 26th, 2010, 03:33 PM   #2
Senior Member
Joined: Jan 2009

Posts: 345
Thanks: 3

Re: Derivatives/linear approximation problem

b. Population in million

We need to find the rate (r), so we divide both sides by 2.1, take the natural log of both sides and divide by 25.

We now have a function.

Using 1970 as a starting point and 1995 as an ending point over the 25 years we can calculate the average rate of change which is normally has a general form of on the open interval

Average rate of change
sivela is offline  

  My Math Forum > College Math Forum > Calculus

approximation, derivatives or linear, problem

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Linear approximation of Non linear system by Taylor series RGNIT Calculus 0 March 20th, 2014 11:21 PM
Linear approximation problem 84grandmarquis Applied Math 2 October 20th, 2013 04:50 PM
need help with linear approximation problem pdeep Calculus 4 November 2nd, 2011 03:11 AM
Derivatives: Differential and Linear approximation HELP ProJO Differential Equations 5 February 24th, 2011 06:28 PM
Derivatives: Linear Approximation Oranges'n'Lemons Calculus 1 February 20th, 2011 09:31 PM

Copyright © 2019 My Math Forum. All rights reserved.