1. On the CIA World Factbook website it says that the world population increases by about...

Transcribed Image Text:

1. On the CIA World Factbook website it says that the world population increases by about 1% each year. This means that the population multiplies by 1.01 each year. There are currently about 7 billion people in the world. a. Find an algebraic model (also known as the equation) for this situation. Remember to clearly define your variables. b. Use your model to predict the world's population in 2035. 2. Comparing Linear and Exponential Models: LINEAR FUNCTIONS i. ii. ii. Complete the table: X y = 3x + 2 0 1 2 3 3. Constructing Linear and Exponential Functions LINEAR FUNCTIONS Write an example of a linear function that is increasing and has a y-intercept of 5. What do the constants 2 and 3 represent? Write an example of a linear function that is decreasing and has a y-intercept of 12. 1. EXPONENTIAL FUNCTIONS Complete the table: X y = 3.2x 0 1 2 3 ii. What do the constants 2 and 3 represent? EXPONENTIAL FUNCTIONS i. Write an example of an exponential function that is increasing and has a y- intercept of 5. ii. Write an example of an exponential function that is decreasing and has a y-intercept of 12. 179 4. Without using a graphing calculator, match the equations and graphs. Explain your reasoning. f(x)=2(1.3) g(x)=2(1.8)" X f(x) 0 25+ 4 20- 5. Use the two tables below. 15+ 10+ 1 2 2 1 3 0.5 X 0 1 2 g(x) 1 0.75 0.50 3 0.25 Analyze each table to determine if it is linear or exponential. Find the function for each table. Show how you determined the function in each case. 6. Complete the following sentences: (a) A linear function is increasing if its slope is (b) A linear function is decreasing if its slope is (c) An exponential function is increasing if its growth factor is (d) An exponential function is decreasing if its growth factor is 180 7. Imagine that the U.S. Congress decided to get serious about decreasing the amount of pollution emitted by cars. As part of their strategy, they plan to pass legislation that requires car manufacturers each year to cut the amount of carbon monoxide released per mile. SUVs will be required to have CO emission per mile reduced to two-thirds of the previous year's level. (a) Make a table showing the carbon monoxide emission level for the first five years after this legislation is passed (starting at zero) for a SUV that currently emits 7290 milligrams of carbon monoxide per mile. (b) Model this situation with a symbolic function. Clearly define your variables. c. Use your calculator to create a table and use it to estimate the number of years it will take before emissions levels are below 5 milligrams of CO per mile. 8. Suppose you invest $3 in a special account that doubles your money every year. (a) Find a function that models this scenario. Did you remember to define your variables? (b) Use your calculator to create a table and use it to estimate the number of years it will be before your account has more than a million dollars in it. 181 9. Use the tables below to do the following: (a) Complete the tables on the left so that they show a linear growth. Complete the tables on the right so that they show an exponential growth. (b) Find an equation for each table of data. (c) Use your calculator's table feature to check your answers to part (b) LINEAR GROWTH X Y X Y 0 1 7 14 08 100 1 110 X 0 1 Y 1000 400 2 2 2 3 3 3 4 4 4 X y X y X y EXPONENTIAL GROWTH 0 7 1 14 0 1 100 110 0 1 1000 400 2 2 2 3 3 3 4 4 4 182 10. Inflation erodes the purchasing power of the dollar. If you have $1.00 today and annual inflation is 5%, next year what costs $1.00 today will cost $1.05. Since - 0.952, in a year your dollar is only worth about $0.952 in today's dollars. Assuming that inflation stays at 5%, this depreciation can be modeled by an exponential function D= 1.00(0.952), where D gives the value or purchasing power of a future dollar in terms of today's dollars and is years from today. How long does it take before your purchasing power cut in half? Answer this question by constructing a graph and a table. Explain how to use each type of model to answer the question. t D(t) 1. On the CIA World Factbook website it says that the world population increases by about 1% each year. This means that the population multiplies by 1.01 each year. There are currently about 7 billion people in the world. a. Find an algebraic model (also known as the equation) for this situation. Remember to clearly define your variables. b. Use your model to predict the world's population in 2035. 2. Comparing Linear and Exponential Models: LINEAR FUNCTIONS i. ii. ii. Complete the table: X y = 3x + 2 0 1 2 3 3. Constructing Linear and Exponential Functions LINEAR FUNCTIONS Write an example of a linear function that is increasing and has a y-intercept of 5. What do the constants 2 and 3 represent? Write an example of a linear function that is decreasing and has a y-intercept of 12. 1. EXPONENTIAL FUNCTIONS Complete the table: X y = 3.2x 0 1 2 3 ii. What do the constants 2 and 3 represent? EXPONENTIAL FUNCTIONS i. Write an example of an exponential function that is increasing and has a y- intercept of 5. ii. Write an example of an exponential function that is decreasing and has a y-intercept of 12. 179 4. Without using a graphing calculator, match the equations and graphs. Explain your reasoning. f(x)=2(1.3) g(x)=2(1.8)" X f(x) 0 25+ 4 20- 5. Use the two tables below. 15+ 10+ 1 2 2 1 3 0.5 X 0 1 2 g(x) 1 0.75 0.50 3 0.25 Analyze each table to determine if it is linear or exponential. Find the function for each table. Show how you determined the function in each case. 6. Complete the following sentences: (a) A linear function is increasing if its slope is (b) A linear function is decreasing if its slope is (c) An exponential function is increasing if its growth factor is (d) An exponential function is decreasing if its growth factor is 180 7. Imagine that the U.S. Congress decided to get serious about decreasing the amount of pollution emitted by cars. As part of their strategy, they plan to pass legislation that requires car manufacturers each year to cut the amount of carbon monoxide released per mile. SUVs will be required to have CO emission per mile reduced to two-thirds of the previous year's level. (a) Make a table showing the carbon monoxide emission level for the first five years after this legislation is passed (starting at zero) for a SUV that currently emits 7290 milligrams of carbon monoxide per mile. (b) Model this situation with a symbolic function. Clearly define your variables. c. Use your calculator to create a table and use it to estimate the number of years it will take before emissions levels are below 5 milligrams of CO per mile. 8. Suppose you invest $3 in a special account that doubles your money every year. (a) Find a function that models this scenario. Did you remember to define your variables? (b) Use your calculator to create a table and use it to estimate the number of years it will be before your account has more than a million dollars in it. 181 9. Use the tables below to do the following: (a) Complete the tables on the left so that they show a linear growth. Complete the tables on the right so that they show an exponential growth. (b) Find an equation for each table of data. (c) Use your calculator's table feature to check your answers to part (b) LINEAR GROWTH X Y X Y 0 1 7 14 08 100 1 110 X 0 1 Y 1000 400 2 2 2 3 3 3 4 4 4 X y X y X y EXPONENTIAL GROWTH 0 7 1 14 0 1 100 110 0 1 1000 400 2 2 2 3 3 3 4 4 4 182 10. Inflation erodes the purchasing power of the dollar. If you have $1.00 today and annual inflation is 5%, next year what costs $1.00 today will cost $1.05. Since - 0.952, in a year your dollar is only worth about $0.952 in today's dollars. Assuming that inflation stays at 5%, this depreciation can be modeled by an exponential function D= 1.00(0.952), where D gives the value or purchasing power of a future dollar in terms of today's dollars and is years from today. How long does it take before your purchasing power cut in half? Answer this question by constructing a graph and a table. Explain how to use each type of model to answer the question. t D(t)