Unit Activity Essays (460 words) - Graph, Graph Theory, Function

Unit Activity Unit 7: Advanced Functions This activity will help you meet these educational goals: Mathematical Practices-You will make sense of problems and solve them, reason abstractly and quantitatively, construct arguments, and model with mathematics. Introduction In this unit, you learned about advanced functions such as quadratic functions and composite functions. You modeled scenarios using these more advanced functions. In this activity, you will analyze real-world situations by modeling them as functions and interpreting their graphs. __________________________________________________________________________ Directions and Analysis Task: Population of a Species The population of a species in the wild in Asia has been decreasing exponentially since 1980. This function represents the population of the species t years after 1980: W(t) = 20,000(0.95t). The Wildlife Refuge Foundation noticed this trend before 1980 and decided to try to help reduce the population decline by breeding the species in captivity. The graph shows the number of these animals that have been born in captivity since 1980. [pic] a. About how long will it take for the number of the species born in captivity to be equal to the number of the species remaining in the wild? Type your response here: b. Create a function to represent the number of the species that have been born in captivity, C(t). Type your response here: c. Assuming that the species has a long life span and that all those born in captivity are still alive today, create a function, P(t), to represent the total number of the species that are alive, both in the wild and in captivity. Type your response here: d. At what point would you say that the program to breed the species in captivity stops the decline in population? Explain. Type your response here: e. If this trend continues, about what will be the total population of the species in the world in 2020? Type your response here: f. How many more of the species will be alive in 2020 because of the breeding program? Type your response here: __________________________________________________________________________ Resources Document any references you used for this project below. At minimum, include a title and URL for any Internet resource: Evaluation Your teacher will use this rubric to evaluate the completeness of your work as well as the clarity of thinking you exhibit. Total Points: 5 |Task: Population of a Species |Task points: 5 | | | | |Estimate where an exponential function and a |1 | |linear function intersect. | | | | | |Write a function from a graph. |1 | | | | |Combine an exponential function and a linear |1 | |function. | | | |1 | |Interpret a graph of the function in terms of the| | |situation. |0.5 | | | | |Solve the function at a certain value. |0.5 | | | | |Solve a linear function at a certain value. | | ----------------------- 2014 EDMENTUM, INC.