IM 6.6.15 Lesson: Equivalent Exponential Expressions
In the table below, find the values of and for different values of . What patterns do you notice?
Evaluate the expression for the given value of x.
when is 10
when is
when is
when is
when is
when is
Find a solution to each equation in the list. (Numbers in the list may be a solution to more than one equation, and not all numbers in the list will be used.)
This fractal is called a Sierpinski Tetrahedron. A tetrahedron is a polyhedron that has four faces. (The plural of tetrahedron is tetrahedra.)
The small tetrahedra form four medium-sized tetrahedra: blue, red, yellow, and green. The medium-sized tetrahedra form one large tetrahedron.
How many small faces does this fractal have? Be sure to include faces you can’t see. Try to find a way to figure this out so that you don’t have to count every face.
How many small tetrahedra are in the bottom layer, touching the table?
To make an even bigger version of this fractal, you could take four fractals like the one pictured and put them together. Explain where you would attach the fractals to make a bigger tetrahedron.
How many small faces would this bigger fractal have? How many small tetrahedra would be in the bottom layer?
What other patterns can you find?