Exponential function with 3 parameters?

[zeion]

Exponential function with 3 parameters??

Homework Statement

A researcher suggests that the population, P, at time t can be modeled by

P(t) = K / (1 + Le^(-Mt)), where K, L and M are parameters.

Use technology to estimate and interpret K, L,and M. Construct the researcher's model using your estimates.

Homework Equations

The Attempt at a Solution

There is a value table given, but I'm not sure how to use it to find the parameters.
The first part asked to derive my own model, which I have done, it turned out to be

P(t) = 561(1.02)^x

 

[eumyang]

There is a value table given, but I'm not sure how to use it to find the parameters.
The first part asked to derive my own model, which I have done, it turned out to be

P(t) = 561(1.02)^x

This doesn't look right. For one, what you have is an exponential model, and what you wrote earlier:

A researcher suggests that the population, P, at time t can be modeled by

P(t) = K / (1 + Le^(-Mt)), where K, L and M are parameters.

... suggests that you need a logistic model. They are 2 different things.

Even though you state that you can use technology, I'd like to see the table of values. If you have a TI-83/84, you can perform a logistic regression easy enough to find K, L, and M. (On the TI-83/84, they will correspond to the values of a, b, and c, I think.)

 

[zeion]

Sorry,

I did not type out the whole assignment.

The table of population:

Year: 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995
Population in Millions: 554.6, 609.0, 657.5, 729.2, 830.7, 927.8, 998.9, 1070.0, 1155.3, 1220.5


The first part, in essence: What types of functions could model the behavior of the graph? Analytically develop one model function that fits the data points on your graph.

I made an exponential model by taking the average of the multiplier of P(t) (and constant Δt 5 years.) that fitted the data points.


How would I find the three parameters using a TI-83/84?
And what do each of them mean?

Thanks.

 

[eumyang]

How would I find the three parameters using a TI-83/84?
And what do each of them mean?

You would hit (STAT) -> 1:Edit to input the data into L1 and L2.
Then hit (STAT) -> (CALC) -> B:Logistic -> (ENTER) -> (ENTER)
(You may have to hit the (ENTER) key more than twice.)

Look up "maximum sustainable population," "limit to growth," or "fixed capacity" to see what K is. I don't recall if there are any special names for the other parameters.

 

[zeion]

Okay thanks for your replies.