1. Exponential Functions and Their Graphs I CAN… Graph exponential functions Evaluate exponential functions Use exponential functions to model and solve real-world problems

2. Paper Folding You have been CHALLENGED!!!! How many times can YOU fold a piece of paper in half?! A prize will be yours if you can fold your paper in half 9 or more times!

3. How many times can you fold a piece of paper in half? Did you know that it is physically impossible to fold it in half more than eight times? The reason is exponential growth… Starting with a piece of paper and folding it in half, you’ll notice that its thickness doubles to become two sheets thick. If you fold it again it becomes four sheets thick. This is double what you had before. In fact, each fold doubles the thickness of the stack of paper. This relationship can be expressed mathematically as 2 x 2 x 2 x..., and so on, or 2 n where n is equal to the number of folds. When the paper is folded once, n equals one, therefore the thickness of the pile is 2 1 or two. When you fold it again, the thickness is 2 2 or 2 x 2 = 4. After the seventh fold, the thickness of the stack is 2 7 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128. What prevents the paper from folding any further is its inability to wrap around the thickness of the stack. If you measure a stack of 10 sheets of paper, you’ll find that they have a thickness of approximately one millimetre. Therefore, each sheet averages 0.1 millimetres thick. If this sheet were folded in half seven times, then its thickness would be 12.8 mm. What if it was possible to continue folding the paper? Amazingly, the stack of paper would be over 1.6 metres thick (as tall as you are), after the 14th fold! In fact, by the 28th fold it would be higher than Mount Everest and only five more folds would see it tower past the Moon (over 400 000 kilometres). Many organisms, such as bacteria, multiply according to this simple mathematical principle. It’s amazing how a simple thing like doubling can cause such a rapid increase. Think about how this could apply to spreading rumors!!!!

4. Number of Folds Number of LayersKilometers Familiar Distance 010.1 x 10 -6 0.004 in 120.2 x 10 -6 0.008 in 240.4 x 10 -6 0.016 in 380.8 x 10 -6 0.032 in Thickness of finger nail 4161.6 x 10 -6 0.064 in 5323.2 x 10 -6 1/8 in 6646.4 x 10 -6 1/4 in 712812.8 x 10 -6 1/2 in Thickness of notebook 825625.6 x 10 -6 1 in 951251.2 x 10 -6 2 in 101,0240.1 x 10 -3 4.1 in Width of hand (w/thumb) 112,0480.2 x 10 -3 8.2 in 124,0960.4 x 10 -3 16.4 in = 1.4 ft Height of a stool 138,1920.8 x 10 -3 32.8 in = 2.7 ft 1416,3841.6 x 10 -3 65.5 in = 5.5 ft Average height of person

5. Number of Folds Number of LayersKilometersFamiliar Distance 1532,7683.3 x 10 -3 10.8 ft 1665,5366.6 x 10 -3 21.7 ft 17131,07213.1 x 10 -3 43 ft Height of 2-story house 18262,14426.2 x 10 -3 86 ft 19524,28852.4 x 10 -3 171.9 ft 201,048,576104.9 x 10 -3 344.2 ft Quarter of Sears Tower 2533,554,4323.42.1 mi Past the Matterhorn (mtn.) 301,073,741,824107.466.7 mi Outer limits of atmosphere 3534,359,738,3683.4 x 10 3 2112.7 mi 401,099,511,627,776109.9 x 10 3 68,288.7 mi 4535,184,372,088,8323.5 x 10 6 2,174,799.2 mi 501,125,899,906,842,624112.5 x 10 6 69,904,259.1 mi Approx. distance to sun

6. Exponential Functions In an exponential function, an original amount is repeatedly multiplied by a positive number called a growth factor If greater than one, the function shows exponential growth If greater than 0 and less than 1, the functions shows exponential decay

7. Exponential Functions