7.5 exponential growth and decay 2016 ink.notebook. February 13, Page 69. Page Exponential Growth and Decay. Standards.

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1 7.5 exponential growth and decay 2016 ink.notebook Page 69 Page Exponential Growth and Decay Lesson Objectives Standards Lesson Notes Page Exponential Growth and Decay Press the tabs to view details. 1

Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes A.SSE.1 I will interpret P(1+r) n as the product of P and a factor A.SSE.3 I will evaluate an exponential function A.

1 I will determine if a function shows exponential growth or decay F.LE.2 I will write an exponential growth or decay equation from a story problem F.LE.2 I will write a compound interest function from a story problem F.

2 Lesson Objectives Standards Lesson Notes Lesson Objectives Standards Lesson Notes A.SSE.1 I will interpret P(1+r) n as the product of P and a factor A.SSE.3 I will evaluate an exponential function A.CED.1 I will create exponential equations that describe exponential growth and decay F.BF.1 I will write an exponential equation from a story problem F.LE.1 I will determine if a function shows exponential growth or decay F.LE.2 I will write an exponential growth or decay equation from a story problem F.LE.2 I will write a compound interest function from a story problem F.LE.2 I will write a simple interest function from a story problem F.LE.5 I will determine the initial amount in an exponential function F.LE.5 I will determine the growth or decay factor in an exponential function F.LE.2 I will write an exponential equation from a table F.LE.2 I will write an exponential equation from a graph Press the tabs to view details. F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. b) Use the properties of exponents to interpret expressions for exponential functions. F.LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input output pairs (include reading these from a table). Press the tabs to view details. Find the value of y when x = 6. Round answers to the nearest tenth. (.1) 1. y = 7(2) x 2. y = 12(1.8) x

Formula to model growth or decay by a constant percent increase or decrease: A(t) = P(1 Final amount initial amount + r) t time rate of increase as a DECIMAL A(t) = P(1 + r) t 1 + r = growth factor

3 Formula to model growth or decay by a constant percent increase or decrease: A(t) = P(1 Final amount initial amount + r) t time rate of increase as a DECIMAL A(t) = P(1 + r) t 1 + r = growth factor (increasing) 1 - r = decay factor (decreasing) Find the value of a savings account after t years for an initial deposit P compounded at an interest rate i. Round to the nearest hundredth.01 Value = P(1 + i ) t 3. t = 8, P = $500, i = 4% t = 10, P = $2500, i = 3%

4 Compound Interest initial amount rate of increase as a DECIMAL A(t) = P (1 + n) r nt time annually = once a year semiannully = twice a year quarterly = 4 times a year monthly = 12 times a year daily = 365 times a year Final amount number of times per year that interest is compounded Find the value of each investment. Round answers to the nearest hundredth. 5. $2300 at 8% compounded daily for 7 years Find the value of each investment. Round answers to the nearest hundredth. 7. The Garcias have $12,000 in a savings account. The bank pays 3.5% interest on savings accounts, compounded monthly. Find the balance in 3 years. $ $800 at 6.2% compounded monthly for 10 years $ $

The cost of a new automobile increases 5% per year. Determine what the cost of a new car would be after each of the following years.

5 7.5 exponential growth and decay 2016 ink.notebook Write an exponential function to model each situation. Find each amount after a specified time. 8) Suppose a new automobile currently costs $10,000. The cost of a new automobile increases 5% per year. Determine what the cost of a new car would be after each of the following years. equation: 1 yr ) 2 yr. 5 yr A city of 140,000 people has 1% annual decrease in population. Determine the City s population after each of the following years. equation: 2 yr yr. 10 yr

6 10) Suppose you invest $1000 in an account paying 5.5% interest compounded annually. Find the account balance after each of the following years. equation: a. 1 yr. b. 5 yr. c. 10 yr On Your Whiteboards On the Worksheet 6

7 Find the value of y when x = 5. Round to the nearest hundredth y = 1000(.5) x 2. y = 12.5(.8) x 3. y = 128(.75) x 4. y = 1536 Homework Write an exponential function to model each situation. Find each amount after a specified time. 5. Suppose one of your ancestors invested $500 in 1700 in an account paying 4% interest compounded annually. Find the balance after each of the following dates y = 6. The starting salary for a new employee is $25,000. The salary for this employee increases by 8% per year. What is the salary after each of the following years? a b c a. 1 yr. b. 5 yr. c. 15 yr y = 7

8 7. Suppose you invest $750 in an account paying 5.25% interest compounded annually. WRITE an equation to find the account balance after x years. 8. A tax revenue that a small city receives increases by 3.5% per year. In 1980, the city received $250,000 in tax revenue. WRITE an equation to determine the tax revenue after x years. 9. Suppose the acreage of forest is decreasing by 2% per year because of development. If there are currently 4,500,000 acres of forest, determine the amount of forest land after each of the following years. a. 3 yr. b. 5 yr. c. 10 yr. y = 10. A $10,500 investment has a 15% loss each year. Determine the value of the investment after each of the following years. a. 1 yr. b. 2 yr. c. 10 yr. y = 11. A city of 2,950,000 people has 2.5% annual decrease in population. WRITE an equation to determine the City s population after x years. 12. A $25,000 purchase has a 12% decrease in value per year. WRITE an equation to determine the value of the purchase after x years. 8

9 A(t) = A(t) = 13. Determine the amount of an investment of $2500 if it is invested at in interest rate of 5.25% compounded monthly for 4 years. 14. Determine the amount of an investment of $100,000 if it is invested at an interest rate of 5.2% compounded quarterly for 12 years. Answers: 1) ) ) y = 500(1 +.04) x, $ , $ , $ ) y = 750( ) x 9) y = (1.02) x, , , ) y = (1 0.25) x 9

3.3 rates and slope intercept form ink.notebook. October 23, page 103. page 104. page Rates and Slope Intercept Form

3.3 rates and slope intercept form ink.notebook page 103 page 104 page 102 3.3 Rates and Slope Intercept Form Lesson Objectives 3.3 Rates and Slope-Intercept Form Press the tabs to view details. Standards