Thurs 2/4 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest...
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Transcript of Thurs 2/4 Lesson 7 – 1 Learning Objective: To graph exponential functions & solve interest...
Homework Log
Thurs
2/4
Lesson 7 – 1
Learning Objective: To graph exponential functions & solve interest problems
Hw: Pg. 439 #10-25 all
2/4/16 Lesson 7 – 1/7 - 2 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. Not
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)
Assignment: 2/4/16
Pg. 439 #10 – 25
Homework Log
Fri
2/5
Lesson 7–1 &7-2
Learning Objective: Solve interest problems
Hw: Pg. 439 # 26 a-b, 27, 29, 45-49 &Pg. 448 # 28-32
2/5/16 Lesson 7 – 1/7 - 2 Exponential Models (Day 2)
Algebra II
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 Annually/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 1. 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 2. 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 3. 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
Compound Interest 4. 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 = 2000 A = 1500 r = 0.04 1500
1.5
Assignment: 2/5/16 Fri
Pg. 439 # 26 a-b, 27, 29, 45-49 &Pg. 448 # 28-32
Find the compound amount if $20,000 is deposited for 8 years in an account that pays interest at 5% compounded continuously
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