Unit 6 : Exponents

Single Power

100

Solve to a single power

5⁶ x 5¹⁴ / 5¹⁰

5¹⁰

200

Solve to a single power

(8⁵)⁶ / 8¹⁰ x 8⁶

8¹⁴

300

Solve to a single power

((2/8)⁵)³

(2/8)15

400

Solve to a single power

(3.77⁷)⁴  /  3.77⁸

3.77²⁰

500

Solve to a single power

(9X³a)¹¹  x  X⁵  /  4X⁸a³  x  X⁷a

95X²⁵a⁷

Simplifying

100

Simplify

(9⁵)⁰

9

200

Simplify

3⁹  x  3^-5

3⁴

300

Simplify

5⁹  /  5¹²

1/5³

400

Simplify

(7^-5)³  x  7³  /  7⁹

7^-21

500

Simplify

b^-4  x  b¹²  /  (b^-3)⁵  x  b⁹

b²

Model Data

100

The first differences of a graph are all constant increasing by a unit of 5. What type of function does this represent?

Linear

200

The second difference of a function follow a added pattern of +6. What type of function does this represent

Quadratic

300

The first/second differences follow a multiplying pattern of x8. What type of function does this represent?

Exponential

400

Given the following equation, what is the y value when x = 10?

y = 7

282,475,249

500

Troy caught a virus. On the first day 50 bacteria cells were present. On the second day they had multiplied to double that amount. And subsequently continue for 10 days until he was able to get antibiotics. How many bacteria does Troy have in his system on the 5th day?

312,500,000 bacteria

Exponential Functions

100

What makes Y = 4^x a function?

When drawn on a graph it passes the vertical line test.

No x values ever have the same y values

200

What is the domain for most functions

{xER}

300

What are the X intercepts for the exponential equation Y = 9^x?

There are no x intercepts

400

Find the equation of any asymptotes.

(A straight line that a curve will approach but never touch)

Y = 0

500

Determine the equation of the function

Input [-3, 0, 4]

Output [8, 1, 0.625]

Y = 0.5^x

Mixed

100

Solve to a single power

(7³)⁷

7²¹

200

Simplify

10⁸  /  10¹²

1/10⁴ or 10^-4

300

Given the following equation, what is y's value at position 4

Y = 5^x + 6

Y = 629

400

Solve to a single power

15¹⁶  x  15⁹  /  15¹⁵

15¹⁰

500

Determine the equation for the following (round to the second decimal place)

Input (-2,0,3)

Output (19,4,3.01)

Y=0.25^x + 3