Homework Log

Fri

2/5

Lesson 7 – 1

Learning Objective: To graph exponential functions & solve interest problems

Hw: Pg. 439 #10, 14, 17 – 22, 26 – 29, CC#45

Homework Log

Fri

2/5

Lesson 7 – 2

Learning Objective: To graph exponential functions & solve interest problems

Hw: Lesson 7 – 2 WS

2/5/16 Lesson 7 – 1 Exponential Models

Algebra II

To graph exponential functions To identify growth vs. decay To solve interest problems

Learning Objective

Laws of Exponents a, b > 0Product RulePower of a Power RuleQuotient RulePower of a Product RulePower of a Quotient RuleNegative Exponents

Exponential Function , ,

Domain (x) – set of all real numbers Range (y) – set of all positive real numbersIf a > 1 If 0 < a < 1

exponential growth

exponential decay

Sketch a Graph1.

x y – 2 – 1 0 1 2

= 1/4 = 1/2

= 2 = 4

= 1

Sketch a Graph2.

x y – 2

– 1

0

1

2

= 4/9 = 2/3

= 3/2 = 9/4

= 1

Sketch a Graph3.

x y – 2 – 1 0 1 2

= – 1/9 = – 1/3

= – 3 = – 9

= – 1

Sketch a Graph4.

x y – 2 – 1 0 1 2

= –2.25 = –1.5

= 3 = 9

= 0

5. Growth (3 > 1)y-int (x = 0) y = 1(0, 1)

Identify Growth or Decay & Find y-intercept

6. Decay (0.95 < 1)y-int (x = 0) y = 1(0, 1)

7. Decay ( < 1)y-int (x = 0) y = 10(0, 10)

Identify Growth or Decay & Find y-intercept

8. Growth ( > 1)y-int (x = 0) y = 0.75(0, 0.75)

Formula for Compound Amount A = compound amountP = Original Principalr = interest rate (% decimal)n = # of compounds per yeart = time in years

Formula for Compound Amountn = # of compounds per year Yearly n = 1 Semi-annually n = 2 Quarterly n = 4 Monthly n = 12 Weekly n = 52Interest made = Compound Amt – Original Amt

Formula for Compound Continuously A = compound amountP = Original Principalr = interest rate (% decimal)t = time in years

Compound Amount 9. Find the compound amount if $15,000 is deposited for 12 years in an account that pays interest at 8% compounded semiannually.P = 15000 t = 12 r = 0.08 n = 2

Order of Operations!

Compound Continuously 10. Find the compound amount if $15,000 is deposited for 12 years in an account that pays interest at 8% compounded continuouslyP = 15000 t = 12 r = 0.08

Compare amount to Ex. #9!

Compound Interest 11. You deposited $2000 in a savings account that pays an annual interest rate of 4%. How much money after 5 years?P = 2000 t = 5 r = 0.04 n = 1

Compound Interest 12. You invest $1000 in a savings account that pays an annual interest rate of 3.5%. How many years to grow it to $1500?P = 1000 A = 1500 r = 0.035 n = 1 1500

1.5

Find the compound amount if $20,000 is deposited for 8 years in an account that pays interest at 5% compounded continuously

Ticket Out the Door

Assignment:

Pg. 456 #12 – 31 odd, 46 – 53, CC#44