Lesson 3 The Name Game Solidify Understanding

Ready

Use rules of exponents to rewrite each of the expressions with only one exponent.

1.

$3^{5} \cdot 3^{7}$

2.

${(6^{4})}^{2}$

3.

$\frac{5^{14}}{5^{3}}$

4.

$\frac{{(2^{5})}^{3}}{2^{9}}$

5.

$y^{a} \cdot y^{b}$

6.

${(x^{a})}^{b}$

7.

$\frac{n^{c}}{n^{d}}$

8.

$\frac{{(b^{n})}^{m}}{b^{k}}$

Find the missing values in each of the geometric sequences. Then write the explicit equation that describes each function.

9.

$x$	$1$	$2$	$3$
$y$	$5$		$45$

10.

$x$	$1$	$2$	$3$	$4$
$y$	$2$			$16$

11.

$x$	$y$
$1$	$3$
$2$
$3$	$75$
$4$

12.

$x$	$y$
$1$	$4$
$2$
$3$
$4$
$5$	$324$

Set

Based on each of the given representations of a function, determine the following.

Is it linear, exponential or neither? (If neither, do not do parts b-d.)
If the function is linear or exponential, state whether it is discrete or continuous.
Identify the rate of change as a slope (common difference) or a growth factor (common ratio).
Write the explicit equation.

13.

The population of a town, $y$ , is $15,000 people$ and is growing by $1.5 %$ per year.

14.

Joan earns a starting salary of $$ 30,000$ per year and will receive a raise of $$ 2,500$ per year for the first $10 years$ .

15.

$3 x + 4 y = - 3$

16.

The number of gifts received each day of “The $12 Days$ of Christmas” is a function of the day. (“On the fourth day of Christmas, my true love gave to me: $4 calling birds$ , $3 French hens$ , $2 turtledoves$ , and $a partridge in a pear tree$ .”)

17.

18.

Side of a Square	Area of a Square
$1 inch$	$1 {in}^{2}$
$2 inches$	$4 {in}^{2}$
$3 inches$	$9 {in}^{2}$
$4 inches$	$16 {in}^{2}$

19.

How many solutions are there for the explicit linear equation, $y = - 6 x + 5$ ? What do solutions for equations like this look like?

20.

What is the proper way to represent all solutions for a given explicit equation?

Go

For each geometric sequence below, find the missing terms in the sequence. Then write an explicit rule for the sequence.

21.

$n$	$1$	$2$	$3$	$4$	$5$
$y$	$2$				$162$

Explicit equation:

22.

$n$	$1$	$2$	$3$	$4$	$5$
$y$	$\frac{1}{9}$			$- 3$

Explicit equation:

23.

$n$	$1$	$2$	$3$	$4$	$5$
$y$	$10$				$0.625$

Explicit equation:

24.

$x$	$1$	$2$	$3$	$4$	$5$
$y$	$g$				$g z^{4}$

Explicit equation:

Find the rate of change (slope) in each of the problems.

25.

$x$	$g (x)$
$- 5$	$11$
$- 3$	$4$
$- 2$	$0.5$
$0$	$- 6.5$

26.

$t$	$h (t)$
$3$	$13$
$8$	$23$
$18$	$43$
$23$	$53$

27.

$n$	$f (n)$
$- 7$	$20$
$- 5$	$24$
$- 1$	$32$
$2$	$38$

28.

$(2, 5) (8, 29)$

29.

30.

$(- 3, 7) (8, 29)$