Exponential Growth Project
A LGEBRA II WITH T RIGONOMETRY
Name ________________________
Date ____________ Pd _________
In this project, you will investigate exponential growth and how it can apply to realworld situations.
I. Exponential Functions (30pts)
1) y  2 x
 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) y  5 x
 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) y  e x
 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 y  ab x . 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)
7)
8)
9)
In 10 years from now, what will the world population be?
In 20 years from now, what will the world population be?
In 50 years from now, what will the world population be?
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
x
1
material in half-lives: y  100  . The 100 comes from us starting with
2
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 Plutonium239?
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?