Lesson 1 The In-Betweeners Develop Understanding

Ready

The sequences below exemplify a multiplicative (geometric) pattern. Fill in the missing values on the table and then write an explicit equation for the pattern.

1.

Term	$1 st$	$2 nd$	$3 rd$	$4 th$	$5 th$	$6 th$	$7 th$	$8 th$
Value	$2$					$64$

Equation:

2.

Term	$1 st$	$2 nd$	$3 rd$	$4 th$	$5 th$	$6 th$	$7 th$	$8 th$
Value	$360$			$45$

Equation:

3.

Term	$1 st$	$2 nd$	$3 rd$	$4 th$	$5 th$	$6 th$	$7 th$	$8 th$
Value	$- 3$							$- 384$

Equation:

4.

Term	$1 st$	$2 nd$	$3 rd$	$4 th$	$5 th$	$6 th$	$7 th$	$8 th$
Value	$972$					$4$

Equation:

Rewrite each of the square roots below by removing repeated factors from under the square root.

For example, $\sqrt{8} = \sqrt{4 \cdot 2} = 2 \sqrt{2}$ .

5.

$\sqrt{75}$

6.

$\sqrt{63}$

7.

$\sqrt{18}$

8.

$\sqrt{98}$

Set

Fill in the missing values of the table based on the growth that is described, then create the explicit equation for the table.

9.

The growth in the table is tripled at each whole year.

Years	$0$	$\frac{1}{2}$	$1$	$\frac{3}{2}$	$2$	$\frac{5}{2}$	$3$	$\frac{7}{2}$	$4$
Bacteria	$2$		$6$

Explicit equation:

10.

The growth in the table is triple at each whole year.

Years	$0$	$\frac{1}{3}$	$\frac{2}{3}$	$1$	$\frac{4}{3}$	$\frac{5}{3}$	$2$	$\frac{7}{3}$	$\frac{8}{3}$
Bacteria	$2$			$6$

Explicit equation:

11.

The values in the table grow by a factor of $4$ at each whole year.

Years	$0$	$\frac{1}{2}$	$1$	$\frac{3}{2}$	$2$	$\frac{5}{2}$	$3$	$\frac{7}{2}$	$4$
Bacteria	$2$		$8$

Explicit equation:

Go

Rewrite the following expressions using exponent rules and relationships so that there is only one exponent in the expression and all exponents are positive. Write your answers in exponential form. (For example: $2^{2} \cdot 2^{5}$ = $2^{7}$ ).

12.

$3^{2} \cdot 3^{5}$

13.

$\frac{5^{3}}{5^{2}}$

14.

$2^{- 5}$

15.

$17^{0}$

16.

$\frac{7^{5}}{7^{2}} \cdot \frac{7^{3}}{7^{4}}$

17.

$\frac{3^{- 2} \cdot 3^{5}}{3^{7}}$