Modeling Population Growth Answer Key

Zariah Luna Name ___________________________________ Date _________________ Modeling Population Growth Introduction: A population is a group of organisms that belong to the same species and live in the same area at the same time. There are no definite boundaries to a population. The boundaries of a population may result from a geographical feature, such as a lakeshore, or a researcher can arbitrarily define them. Population growth is determined by three factors: the number of births, the number of deaths, and the number of individuals entering or leaving the population. In this activity, you will use your knowledge of mathematical equations to plot the growth of a population over time. Purpose: 1. To calculate the growth of a population over time and plot the data on a graph. 2. To observe the effect of the carrying capacity on population size. 3. To distinguish between exponential growth and logistic growth. Getting Started: You have been asked to determine the size and the growth rate of a population of rabbits over a 20-year period. You must use the following information to determine the size of the population each year. You will graph your data and answer the follow-up questions. The Rabbit Population Statistics • The initial population size in year 0 is 75 rabbits. • Rabbit The birth rate each year per 100 rabbits in the population is 50. The Population • The death rate each year per 100 rabbits in the population is 30. • There is no migration. Follow these steps to model and calculate the growth rate in a population of rabbits: 1. According to the information in the above box, will the rabbit population increase or decrease each It will increase each year because there are more rabbits being born year? How do you know? ______________________________________________________________________________________ than dying. ____________________________________________________________________________________________________________________ 2. Calculate the percent increase in the population each year. Show your work in the space below. % change in population size = (Birth Rate – Death Rate) / 100 rabbits 50 - 30 = 20 20/100 = 0.2 3. Given the percent increase calculated in step 2 and the number of rabbits present in year 0, by how many rabbits will the population increase in the first year? Show your work. 0.2 x 75 = 15 rabbits 1 4. At the end of year 1, what is the total size of the rabbit population? Show your work. 75 + 15 = 90 rabbits 5. Write a word equation for determining the population size in each year based on the calculations used in steps 3 and 4. The population increase is 0.2% and year 0 initially had 75 rabbits. In the next year (year 1), it would increase by 15, making the population of rabbits 90. 6. Fill in the data table on page 3 with the information you know about year 1. You must show your work and the answer in the Population Size column. 7. Ready to calculate the population size each year? Wait! There is another piece of vital information! The rabbits have limited resources available to them. The rabbits live in an area that can only support 600 rabbits. When the population reaches 600 rabbits, the birth rate and the death rate will be reversed. The birth rate per 100 rabbits will be 30. The death rate per 100 rabbits will be 50. The population a) What happens to a population when the death rate is higher than the birth rate? ____________________ would decrease. ________________________________________________________________________________________________________________ b) What will be the percent decrease given this new information? -0.2 c) Write a word equation that will calculate the population size when the death rate is higher than the birth rate. (b-d)/100 8. You have now written two equations: When the birth rate is larger than the death rate. a) When will you use the equation from step 5? _____________________________________________________________ When the death rate is higher than the birth rate. b) When will you use the equation from step 7c? ___________________________________________________________ 9. Using these two equations, fill in the data table on page 3 for all years shown. You must show your work and your answers to receive credit. Round your answers to a whole number of rabbits! 2 Data Table: Population Change Over a 20-Year Period YEAR 0 Population Size: Show calculation and answer 75 (given) 1 75 + (75x0.2) = 75+15= 90 2 90 + (0.2x90) = 90+18= 108 3 108 +(108x0.2) 108 + 21.6 = 130 4 130 + (130x0.2) 130 + 26 = 156 5 156 + (156x0.2) = 156 + 31.2 = 187 6 187 + (187x0.2) 187 + 87.4 = 224 7 224+ (224x0.2) = 269 8 269 + (269x0.2) =323 9 323 + (323x0.2) = 388 10 388 + (388x0.2) = 466 11 466 + (466x0.2) = 559 12 559 + (559x0.2) = 671 13 671 + (671x-0.2) = 537 14 537 + (537x-0.2) = 430 15 430 + (966x-0.2) = 236 16 236 + (236x0.2) = 283 17 283 + (283x-0.2) = 226 18 226 + (226x-0.2) = 181 19 181 + (181x-0.2) = 145 20 145 + (145x-0.2) = 116 ** Round to a whole number of rabbits. Graphing Your Data: Make a line graph showing your data on population growth over the 20-year period. • Determine what variable to place on the x-axis and the y-axis. • Label each axis. • Scale each axis appropriately. • Title your graph. • Plot points as accurately as possible. 3 Populations of Rabbits Per Year Title: ________________________________________________________________________________________ 10. Define the term “carrying capacity”. Draw a line on your graph above representing the carrying The max number of things that can be held in that place. capacity of the rabbits. Label the line. _______________________________________________________________________ ____________________________________________________________________________________________________________________ resources, and other predators. 11. What three factors determine the growth rate of a population? Space, ____________________________________________ ____________________________________________________________________________________________________________________ It had been increasing. 12. Name and describe the type of growth that is occurring during the first 12 years. _______________________ 4 ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ It started to decrease. 13. Name and describe the type of growth that occurs after the 12 year mark. _______________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ 14. What will happen to the birth rate and the death rate of a population when: a) resources are abundant? ___________________________________________________________________________________ b) resources are limited? ______________________________________________________________________________________ 15. List three factors that might determine the carrying capacity of a population. Ø ____________________________________________________________________________________________________________ Ø ____________________________________________________________________________________________________________ Ø ____________________________________________________________________________________________________________ 16. Describe what happens in a population in the years after the carrying capacity is reached. After the carrying capacity has been reached, the population starts to go down. ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________ 17. Explain what changes you would see in your graph if, in year 6, twenty new rabbits immigrated into this population. _________________________________________________________________________________________________ 18. Assume that a pair of mice produces 6 offspring, and that half the offspring are male and half are female. Further, assume that no offspring die. If each pair of mice breeds only once, how many offspring would be produced each year for 5 years? Year 1: ___________________________________________________________________________________________________________ Year 2: ___________________________________________________________________________________________________________ Year 3: ___________________________________________________________________________________________________________ Year 4: ___________________________________________________________________________________________________________ Year 5: ___________________________________________________________________________________________________________ Copyright © Amy Brown Science 5