MM212 Population Models Unit 10 Discussion
Population Models
Post 1: Initial Thread
Go to a website such as the U.S. Census Bureau’s data page and determine the population of your county/parish/borough for the year 2000, and then for another year after that time.
Let the variable t represent the number of years since the year 2000. Therefore, t = 0 represents the year 2000, t = 1 represents the year 2001, and so on.
- State your county/parish/borough name and the website you used.
- Write your data as two ordered pairs (t, P).
Now, you will create a population model based on these two data points! Population growth can be modeled by an exponential function of the form:
- Substitute the population for the year 2000 for P0, and write the function.
- Substitute the population value and t value from the second ordered pair into the function for P(t) and t, respectively.
- Solve the equation for the value of k. Show each step in your calculations.
Round k to four decimal places. - Substitute the values of Po and k in the original model, P(t) = Poekt, and write the function. You should now have a function that models the population of your county/parish/borough as a function of the time in years since 2000.
Post 2: Reply to a Classmate
Choose one classmate’s post that you find interesting.
- Using your classmate’s function, estimate the population of that county/parish/borough for the current year. Remember that t = the number of years since 2000. State your value of t and your classmate’s population model.
- Solve the equation for the current population. Show each step in your calculations and round to the nearest person.
- Does your calculated population match with the actual population in their county/parish/borough? You will need to research the current population online.
Post 3: Reply to Another Classmate
Choose another classmate’s response and reply to their post.
- Assuming that the population follows your classmate’s exponential population model, estimate the population of their county/parish/borough for the year 2050.
- Explain the result. Is this surprising or reasonable? Is a strict exponential model reasonable for population growth?
Return to Unit 10 Discussion Instructions
MM212 Population Models Unit 10 Discussion Answer
I used time and population to obtain my two ordered pairs of (0, 298,084) and (10, 330,844) to make a population model where P(t)= P0 is the starting population for t= 0, P(t) is the population at the time, t, and k is the growth constant.
The starting population pair is (0, 298,084) for P0,…..
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