Bellwork If you have 120 m of fencing to make three side-by-side enclosures, what is the maximum area that you can enclose? 450 sq m.

BellworkIf you have 120 m of fencing to make three side-by-side enclosures, what is the maximum area that you can enclose?

450 sq m

EXPONENTS AND LOGS

•Integral, rational and real exponents

•Exponential growth and decay

•Natural exponential functions (e)

•Compound Interest

•Logs

Integral Exponents5.1

•Define the Laws of Exponents (p. 170)•Apply the Laws of Exponents

Exponent Rules(Page 170)

• When multiplying – add exponents

• When dividing – subtract exponents

• Power to a power – multiply exponents

• Negative exponent – flips upside down

Examples: No Calculator!!!

28

2

4

3

3)3( 23 )5( x

8 3

4

n n

n

More Examples of Simplifying Exponents

)( 353 xxx

4

23

2

46

x

xx

43 2

2 3

x y

x y xy

1

1

1 y

y y

SIMPLIFY BY USING POWERS OF THE SAME BASE:

8 5

1

2 4

16

3

2

25 5

125

n

n

Exponential Growth and Decay

If you know that the cost of attending collegehas been averaging a 10 percent increase every yearfor the last 10 years, how much would it cost to attendcollege today if it cost your friend $30,000 7 years ago?

Exponential Growth and Decay Formula

0( ) 1t

A t A r Initial amount

Rate How long?

If you know that the cost of attending collegehas been averaging a 10 percent increase every yearfor the last 10 years, how much would it cost to attendcollege today if it cost your friend $30,000 7 years ago?

7( ) 30,000(1 .10)A t

Initial amount

Rate How long?

$58,461.51

In a city, the value of a house is increasing at a rate of 16% annually.

Find the value of a house currently worth $100,000

after 4 years.

$181,063.94

In how many years will the value of the house be

approximately double the current cost?

What was the approximate price 3 years ago assuming this

increase had been constant?