Exponential Growth Project Name ______
Algebra II with Trigonometry Date ______Pd ______
In this project, you will investigate exponential growth and how it can apply to real-world situations.
I. Exponential Functions (30pts)
1)
§ Create a table of values for x=-2,-1,0,1,2,3,4,5,6,7,8,9,10.
§ Describe with words the pattern in the y column.
§ Graph this function on your calculator or graphing software. Attach your graph.
§ What is the function’s domain (possible x-values)?
§ What is the function’s range (possible y-values)?
§ What is the y-intercept?
§ Is there an x-intercept?
§ Is the function periodic? If so, what is its period and amplitude?
2)
§ Create a table of values for x=-2,-1,0,1,2,3,4,5,6.
§ Describe with words the pattern in the y column.
§ Graph this function on your calculator or graphing software. Attach your graph.
§ What is the function’s domain (possible x-values)?
§ What is the function’s range (possible y-values)?
§ What is the y-intercept?
§ Is there an x-intercept?
§ Is the function periodic? If so, what is its period and amplitude?
3)
§ Research what the number e is. Check with Mr. Yates to see if what you have found is correct.
§ Create a table of values for x=-2,-1,0,1,2,3,4,5,6,7,8.
§ Describe with words the pattern in the y column.
§ Graph this function on your calculator or graphing software. Attach your graph.
§ What is the function’s domain (possible x-values)?
§ What is the function’s range (possible y-values)?
§ What is the y-intercept?
§ Is there an x-intercept?
§ Is the function periodic? If so, what is its period and amplitude?
II. Human population (30pts)
1) Find out what the current world population is.
2) The general form of an exponential function is . Notice the x must be the exponent, not the base! The a is the initial value, that is whatever you start with (for example, world population in the year 2008). The b is the growth rate.
3) Human population is growing 1.167% a year. Express this as in decimal notation (think 50% = ______, 10% = ______, 1% = _____).
4) Add 1 to this number to get your growth rate.
5) Write your equation down here. Check with Mr. Yates that this is correct.
6) In 10 years from now, what will the world population be?
7) In 20 years from now, what will the world population be?
8) In 50 years from now, what will the world population be?
9) In 100 years from now, what will the world population be?
10) What was the population in 1900, according to this model (1900 is 108 years ago, so enter a value of -108)?
11) What was the population in 1800, according to this model?
12) Find the real world population in 1900 and 1800. How does this compare to your prediction from the model?
13) Exponential growth is a decent model for population growth with unlimited resources. What does this mean?
14) Are resources for us really unlimited? Why or why not? Will exponential growth continue to be a good model?
15) Find out the current United States population. Also find the current Maryland population, and the population of Baltimore City.
III. Radioactive decay (20pts)
1) If your base for the exponent is a fraction, less than 1, what is happening is not growth but decay.
2) In chemistry and physics, you learn that certain radioactive elements (like those used in nuclear bombs) are unstable and decay quickly. This is measured in half-lives. Research the half-life for Plutonium-239.
3) To see an equation for half-life, we can count the percentage left of a material in half-lives: . The 100 comes from us starting with 100% of the material. How much plutonium is left after one half-life? Plug x=1 into the equation. If your answer from the above equation is not 50%, something is wrong! How long is one half-life for Plutonium-239?
4) Sketch or print the graph of this exponential function.
5) How much plutonium is left after the time of two half-lives? How long is that for Plutonium-239?
6) How much is left after 3 half-lives? How long is that for Plutonium-239?
7) When will there be 20% left? Graph the earlier equation along with the equation y=20, then find the intersection. How long is this for Plutonium-239?
8) When will there be 5% left? How long is that for Plutonium-239?
9) When will there be 1% left? How long is that for Plutonium-239?
10) Will the plutonium ever disappear entirely?