Thread: Population Logarthmic Growth Question

I have a problem to do and I don't quite understand it. It's based off the population growth in China. It says that a researcher suggests that the population P, can be modeled by

P(t) = k/(1+Le^-Mt)

Where K, L, and M are parameters

It then says: use technology to estimate and interpret K, L, and M.

What I don't understand it what does it mean to use technology to estimate and interpret the parameters. What do the parameters mean?

Thanks for any help

Originally Posted by JMathHelp

I have a problem to do and I don't quite understand it. It's based off the population growth in China. It says that a researcher suggests that the population P, can be modeled by

P(t) = k/(1+Le^-Mt)

Where K, L, and M are parameters

It then says: use technology to estimate and interpret K, L, and M.

What I don't understand it what does it mean to use technology to estimate and interpret the parameters. What do the parameters mean?

Thanks for any help

Use technology presumably means use the internet to find out the population, growth rate etc of china. You should probably graph population over time, as this is what the question is asking for.

Then, you can also use graphing programs to test the given equation against the graph.

Parameters are variables you change to affect the outcome. The idea is that you change the values of K, L, and M to fit a graph of china's population over time.

Thanks. I did try to graph it, but I got something that looks almost linear. That's why I'm a little confused why there's a inverse logarthmic problem.

Originally Posted by JMathHelp

Thanks. I did try to graph it, but I got something that looks almost linear. That's why I'm a little confused why there's a inverse logarthmic problem.

Perhaps you're not looking back far enough.

Here is a nifty little tool for data visualisation(they provide the data too!): Gapminder: Unveiling the beauty of statistics for a fact based world view. - Gapminder.org

Here is the graph I got for China's population since the 1600s.
www.bit.ly/bHd8qU

Originally Posted by JMathHelp

I have a problem to do and I don't quite understand it. It's based off the population growth in China. It says that a researcher suggests that the population P, can be modeled by

P(t) = k/(1+Le^-Mt)

Where K, L, and M are parameters

It then says: use technology to estimate and interpret K, L, and M.

What I don't understand it what does it mean to use technology to estimate and interpret the parameters. What do the parameters mean?

Thanks for any help

You need to use the population of China for at least three times then using a spread sheet or something similar find k,L and M so that the expression for the population fits the data.

k - is the population at time t

CB

@Gusbob. Yeah, I should have said this before but the problem only gives a certain set of data. When I graphed the entire data table they gave us, I got something looking approximately linear.

@CaptainBlack. Wait I don't quite understand. How is K the population at time t. Isn't that P(t) ?

Hey I had problems with the same thing. But fortunately I found this page M119 Project – Modeling with Logarithmic and Logistic Functions it will tell u how to calculate K, L, n M using TI-83 Hope it helps