Question 1119627: Growth rates can be characterized by two different growth curves:
• LINEAR - linear growth occurs at a constant rate. Many increases or decreases occur at linear rates. An example would be having your salary increase by $1000.00 per year.
• EXPONENTIAL - exponential growth occurs at an increasing rate through time. An example would be having your salary increase (or decrease) at a rate of 5% per year.
Populations have the reproductive potential to increase at an exponential rate. However, population is limited by many factors, including availability and quality of water, food, shelter, and territory, as well as natural and human-made changes in habitat. It is difficult to quantify these limiting factors when modeling population growth.
As an example, in 1935 Wyoming had no Merriman’s turkeys within its borders. A decision was made to plant 46 turkeys in a mountainous area of the state. This activity will provide an opportunity to compute the possible growth of the turkey population during subsequent years after the planting.
Turkey Population Data
Generation Starting Population + Increase Final Population
1 46 250 296
2 296 250
3
4
5
6
7
8
9
Linear Growth Model
1. Complete the table by computing the size of the population of these turkeys in Wyoming using the following assumptions:
a. Every year, 250 offspring are produced by the turkey population.
b. No turkeys emigrate, or leave the area.
c. There were no diseases, shortages of food, or shortage of space that limited the population.
2. Graph the turkey population over the nine generations. Generation is on the x-axis, population on the y-axis. A set of axes is included on the next page.
3. Use your data and/or graph to find a linear model for the population growth. Write the model below.
4. Use your model to predict the population of generation 15. Show your work.
5. Do you believe this is an accurate model of the growth of these turkeys? Explain.
6. Look back the three assumptions given, pick one and give a reason why it is flawed.
7. What is another limiting factor that is not accounted for in this model?
Exponential Growth Model
8. Complete the table by computing the size of the population of these turkeys in Wyoming using the following assumptions:
a. No turkeys left the general area during the first five years.
b. There was no disease, shortage of food or habitat limiting the population.
c. There were equal numbers of females and males in each hatch.
d. Each mature female produces 10 eggs per year. Each egg survives.
e. Turkeys do not reach sexual maturity until they are one year old.
f. All turkeys only survive five years.
g. The original population of turkeys was each 1 years old and sexually mature.
h. There were 23 females and 23 males originally introduces into the population.
Turkey Population Data
Generation Starting Population - Five year olds
(die of old age) - Last Year’s Hatch
(sexually immature) = Total breeding population Total Breeding Pairs
(Divide by 2) Offspring
Hatched
(10 eggs/ pair) New Total Population
= Offspring
+ breeding population + last year’s hatch
1 46 0 n/a 46 23 230 276
2 276 0 230 46 23 230 506
3 506
4
5
6
9. Graph your results from the second turkey population model. Remember, generation is the x-axis, population the y-axis. A set of axes is included on the next page.
10. Use your data and/or graph to find an exponential model for the population growth. Write the model below.
11. Use your model to predict the population of generation 15. Show your work. Round to the nearest integer.
12. Do you believe this is a more or less accurate model than the linear growth model? Explain why.
Answer by solver91311(24713)   (Show Source):
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