Lesson 3 Be the Lizard Wizard Develop Understanding

Ready

Write the following with an exponent.

1.

$\sqrt[5]{x}$

2.

$\sqrt[7]{s^{2}}$

3.

$\sqrt[3]{w^{8}}$

4.

$\sqrt[3]{8 r^{6}}$

5.

$\sqrt[5]{125 m^{5}}$

6.

$\sqrt[3]{{(8 x)}^{2}}$

7.

$\sqrt[3]{9 b^{8}}$

8.

$\sqrt{75 x^{6}}$

Rewrite with a fractional exponent. Then find the answer.

9.

$\log_{3} \sqrt[5]{3} =$

10.

$\log_{2} \sqrt[3]{4} =$

11.

$\log_{7} \sqrt[5]{343} =$

12.

$\log_{5} \sqrt[5]{3,125} =$

Set

Find a formula for the functions in each table.

13.

$0$	$217$
$1$	$317$
$2$	$463$
$3$	$675$
$4$	$986$
$5$	$1,440$

14.

$0$	$40,000$
$1$	$24,000$
$2$	$14,400$
$3$	$8,640$
$4$	$5,184$
$5$	$3,110$

15.

$0$	$16$
$1$	$14.08$
$2$	$12.39$
$3$	$10.9$
$4$	$9.6$
$5$	$8.44$

16.

The table shows the amount of money a person had in their savings account at age $20 years$ , $25 years$ , and so on, up to age $45$ .

$t$	$20$	$25$	$30$	$35$	$40$	$45$
$f (t)$	$1,000$	$1,200$	$1,440$	$1,728$	$2,073.6$	$2,488.32$

a.

Find a formula for the function in the table.

b.

What does $t$ represent in the formula you wrote?

c.

Find the formula for the function if $t$ represents $1 year$ . Explain how the change factors $1.2$ and $1.037$ are related.

d.

Use $f (t) = 1,000 {(1.2)}^{t}$ where $t$ represents $5 years$ to write an equivalent expression to show the yearly change.

Go

Convert to logarithmic form.

17.

$2^{9} = 512$

18.

$10^{- 2} = 0.01$

19.

${(\frac{2}{3})}^{- 1} = \frac{3}{2}$

Write in exponential form.

20.

$\log_{4} 2 = \frac{1}{2}$

21.

$\log_{\frac{1}{3}} 3 = - 1$

22.

$\log_{\frac{2}{5}} \frac{8}{125} = 3$