Exponential Functions

Exponent Properties

100

Simplify the expression:

4³ * 4²

4^{3 +2} = 4⁵

200

Simplify the expression:

[(-4)³]²

-4^{3 * 2} = -4⁶

300

Simplify the expression

(k³)^-2

k^{3 * -2} = k^-6

         = 1/k⁶

400

Simplify the expression:

(4r³/2r⁵)

(4r³/2r⁵)

= 2r^-2

= 2/r²

500

Simplify the expression.

(5x⁰/ 10x^-3y²)²

(5x⁰/ 10x^-3y²)²

= 1x⁶/ 4y⁴

Growth/ Decay/ Compound Interest

100

Is this function an exponential growth or decay?

y = 4(1.65)^t

Growth 

200

What is the percent rate of change in this function?

y = 10(0.05)^t

.95 = 95%

300

The house is worth 9,000 dollars and the price increases by 20%. Write a function that represents the value of house after t years. 

y = 9,000( 1+.2)^t

400

You buy a used car for $6599. Its value decreases by 12% every year.

(a) write the function that represents the value y of the car after t years.

(b) What is the value of the car after 2.5 years?

(a) y = 6599(1 - .12)^t

(b) y = 6599(1 - .12)^2.5

           ⁼ $4794

500

You deposit $2000 in an account that pays 4% annual interest. Find the balance after 8 years if the interest is compounded semi-annually.

2000( 1 + .04/2)^2*8

= $2745.57

Rational Exponents

100

A rational exponent is an exponent that is a fraction...

yes or no 

yes

200

a^1/n,  the denominator n is the ___________

index 

300

Evaluate the expression.

100^3/2

1000

400

Rewrite the expression in exponent form and evaluate.

(radical 9)³

9^3/2

= 27

500

Evaluate the expression.

12^-1/2 * 12^5/2

= 12^{(-1/2) + (5/2)}

= 12 ^4/2

= 12²

= 144

Graphing Exponential Functions

100

The curve of an exponential growth graph is ___________, while the curve of an exponential decay graph is _______________.

increasing 

decreasing 

200

Which of the following does not represent an exponential function?

a. y =(0.25)^x

b. y =4* (3/2)^x

c. y= 2x+4

d. y= (0.5)^{x +2}

c. y = 2x+4

300

Tell whether the table represents an exponential function. Why?

x: -1 | 0 | 1 | 2

y: 2 |  8 | 32 | 128

Yes because the y is being multiplied by 4.

400

Graph the function:

y = 4 * (0.5)^x

Answer shown on the board...

Graph should be decreasing towards the right with the y-intercept at 4, (0,4).

500

Without graphing, explain how the graph of the given functions are related to the graph f(x)= (0.5)^x.

n(x)= -4 (0.5)^x

The graphs are the same, but the only difference is that the second graph has a y-intercept of -4. Therefore this graph passes through the y axis at (0,-4).

True or False

100

The formula for exponential growth is y = a(1-r)^t.

False

y = a(1+r)^t

200

The formula for exponential decay is y = a(1-r)^t.

True 

300

When there is no number shown in the index, that means that it's always 1. 

False. 

It is always 2 (square root)

400

You can tell when a table represents an exponential function when the y's add up by a number.

False.

You can tell when the y's multiply by a number.

500

In a compound interest problem, the n is determined by the number of times interest is compounded per year.

True