15.1: Up or Down?
- Find the values of $3^x$ and $\left(\frac13\right)^x$ for different values of $x$.
row 1 $x$ $3^x$ $\left(\frac13\right)^x$ row 2 1 row 3 2 row 4 3 row 5 4
- What patterns do you notice?
Let's investigate expressions with variables and exponents.
row 1 | $x$ | $3^x$ | $\left(\frac13\right)^x$ |
---|---|---|---|
row 2 | 1 | ||
row 3 | 2 | ||
row 4 | 3 | ||
row 5 | 4 |
Evaluate each expression for the given value of $x$.
$3x^2$ when $x$ is 10
$3x^2$ when $x$ is $\frac19$
$\frac{x^3}{4}$ when $x$ is 4
$\frac{x^3}{4}$ when $x$ is $\frac12$
$9+x^7$ when $x$ is 1
$9+x^7$ when $x$ is $\frac12$
Find a solution to each equation in the list that follows. (Numbers in the list may be a solution to more than one equation, and not all numbers in the list will be used.)
List:
$\frac{8}{125}$
$\frac{6}{15}$
$\frac{5}{8}$
$\frac89$
1
$\frac43$
2
3
4
5
6
8
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.
In this lesson, we saw expressions that used the letter $x$ as a variable. We evaluated these expressions for different values of $x$.
We also saw equations with the variable $x$ and had to decide what value of $x$ would make the equation true.