Ch 6 Jeopardy- Honors

Exponent Rules

100

Simplify

(2 x^-4 y²)^-3 

x¹² / 8y⁶

200

Simplify:

3 x^-2 y

--------

6 x y^-3 

y⁴

----

2x³

300

24x²y³ *  2x⁸

-----------------

      6x¹²y⁵ 

8 / x²y² 

400

Simplify:

(-5 x² y^-1 )²

---------------

10 x y²

5 x³

----

2 y⁴

Writing Formulas

100

Write the formula:

X   -1    0    1    2

Y   1/4   1   4    16

y = 4^x 

200

Write the formula:

X   -1    0    1    

Y   1/2  4   32

y = 4 (8^x)

300

Write the formula:

X   -1    0    1    

Y   12    4   4/3

y = 4 (1/3)^x 

400

X   0    1

Y   6    4

y = 6 (2/3)^x

Word Problems

100

Write the simplified formula. Then solve:

A sourdough starter began with 20 grams of dough. It then doubled in size every 2 hours. How much dough was there after 6 hours?

y = 20(2)^x

y = 20(2)³ = 160 grams

200

Write the simplified formula:

Bob puts $12,000 in a savings account that earns 1.8% annual compound interest.

y = 12,000 (1.018)^t

300

Write the simplified formula:

A study found that a car depreciates in value by 15% annually.  Write the formula representing the value of a car that originally cost $26,500. Then find how much the car is valued for after 3 years.

y = 26500 (0.85)^t

y = 26500 (0.85)³ = $16,274.31

400

Write the simplified formula.  Then solve:

The population of a town is decreasing by 3% annually.  In 2000, there were 17000 people in the city.  Find out how many people they predict to be left in 2025.

y = 17000 (0.97)^t

y = 17000 (0.97)²⁵ = 7,939 people

Making Graphs

100

y = 5(2)^x

x  -2     -1    0    1   2

y  1.75  2.5  5   10  20

200

y = 4 (1/2)^x

x  -2     -1    0    1   2

y  16     8     4    2   1

300

y = 1/4 (2)^x

x  -2      -1      0    1    2

y  1/16  1/8  1/4  1/2   1

400

y = 3 (1/5)^x

x  -2    -1    0    1    2

y  75    15   3   0.6  0.12

Exponential Equations

100

5^4x-1 = 5⁶

x = 7/4 or x = 1.75

200

4^-x+2 = 64

x = -5

300

8^x-1 = 2^x+2

x = 2.5

400

(1/9)^x+2 = 27^{2x - 1}

x = -1/8