My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
May 9th, 2017, 01:10 PM   #1
Joined: Feb 2017
From: henderson

Posts: 36
Thanks: 0

In 2009, the population of Hungary was approximated

In 2009, the population of Hungary was approximated by p=9.906(0.997)^t
where P is in millions and t is in years since 2009. Assume the trend continues.

A) what does the model predict for the population of Hungary in the year 2020?

B) how fast (in people/year) does this model predict Hungary's population will be decreasing in 2020?

Can anybody explain how to do A and B please?
Answers do not need to be given. I just need to know how to solve.

Last edited by skipjack; May 10th, 2017 at 09:48 AM.
Bobbyjoe is offline  
May 9th, 2017, 01:21 PM   #2
Joined: Feb 2015
From: Southwest

Posts: 96
Thanks: 24

A should be easy enough, it's just algebra with some interpretation. t is given in years since 2009 and they ask what is the expected population in 2020.

So if t=0 is 2009, what is t when it's 2020?

As for B, you are really wanting the derivative of the function and putting t in that represents 2020.

I've seen your other questions on the forum and I get you are struggling to understand the derivative. Try to think about it in this context for this problem as t represents years, when you take the derivative you are saying what is the change in population per year. It's per year since t represents each year from 2009.

Derivatives represent the change in a function with respect to an input. In this case, your input is years. Don't misinterpret what I'm saying here, p'(20) would not be change in population in twenty years, but the change in population per year at t=20 or 2029.

Hopefully this helps, work it out a bit, and if you're still struggling put up your work and I or someone else will help you through it.

Last edited by skipjack; May 10th, 2017 at 09:52 AM.
phrack999 is offline  
May 10th, 2017, 03:50 AM   #3
Math Team
Joined: Jan 2015
From: Alabama

Posts: 2,579
Thanks: 668

$\displaystyle 0.997^t$ can be written as $\displaystyle e^{\ln(0.997^t)}= e^{t \ln(0.997)}$ so its derivative is $\displaystyle \ln(0.997) e^{t \ln(0.997)}= \ln(0.997) (0.997^t)$.

Last edited by skipjack; May 10th, 2017 at 09:50 AM.
Country Boy is offline  

  My Math Forum > College Math Forum > Calculus

2009, approximated, hungary, population

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
|x+|2x+|4x|||=2009 mattematicarka Algebra 3 February 4th, 2013 04:04 PM
mixed PD derivative approximated by finite differences silvia_petkova Applied Math 2 July 6th, 2012 02:06 AM
Show 2009 is not prime rnck Math Events 9 August 24th, 2011 12:26 PM
analytic function, approximated normally zelda2139 Complex Analysis 0 April 28th, 2010 09:32 PM
2009 and perfect cube(s) K Sengupta Number Theory 1 March 6th, 2009 07:31 AM

Copyright © 2017 My Math Forum. All rights reserved.