New Paltz Middle School



Unit 8: ExponentialLesson 3: Simple vs Compounded.Objectives:I can identify linear, exponential and quadratic functions examining tables of data.I can write a linear, quadratic and exponential function examining a table of data.I can write a linear, quadratic and exponential function examining a graph.I can use the calculator to write functionsAgenda:Do Now: Quadratics and TransformationClass DiscoveryLinear vs. Exponential vs. Quadratic tablesUsing the calculator to write equationsPracticeFocus Questions:How can identify the nature of a function examining data in a table?How can we write linear, exponential and quadratic functions expressed in a tables of data or a graph?How can I use the calculator to write my functions?Vocabulary: Transformationsystem of equationsLinear vs. quadratic functionsHomework: HW 8-3 + Quiz on Lesson 1 and 25343525-27622500Do Now: Factoring February3x3-27x b. x4+5x2-36 Look at the following function and identify the following:fx=2x+5 fx=3(5)x Name the function; identify the initial value and the rate of change/ Decay or growth factor.Graph both functions: Compounded vs Simple: which is a better option: Lesson 8-3CompoundedValue of nFormula usedSimple Interest – Interest is calculated once per year on the original amount borrowed or invested. The interest does not become part of the amount borrowed or owed (the principal).N/AA=P1+rtCompound Interest – Interest is calculated once per period on the current amount borrowed or invested. Each period, the interest becomes a part of the principal.Money can be compounded:A=P(1+rn)n.tYearlyn=1Quarterlyn=4Monthlyn=12Dailyn=365Weeklyn=52Discuss your options:If you have $??? to invest for 10 years, would you rather invest your money in a bank that pays 7% simple interest or 5% interest compounded annually?A=P(1+rn)n.tA=P1+rtStudent Friendly Bank pays a simple interest rate of 2.5% per year. neighborhood Bank pays a compound interest rate of 2.1% per year, compounded monthly. Which bank will provide the largest balance A=P(1+rn)n.tA=P1+rta. If you plan to invest $??, ??? for 10 years? b. For 20 years?c. Estimate when the first option will generate at least $14000?James needs $200 to start a snow cone stand for this hot summer. He borrows the money from a bank that charges 4% simple interest a year.Write down the equation that will help you identify the money earned f(x) after x years?How much will he owe if he waits 1 year to pay back the loan? If he waits two years? 3 years? 5295900-32385000Class Discovery: With a Partner: Look at the following tables -1603122336 411 Table I Table 2 Table 3Graph the above functions from the given tables: Using the calculator to identify functions: For each Table do the following:Hit the STAT key on your calculator. Go to 1: EDITIn L1, enter all the x values in the table.In L2, enter all the y values in the table. Hit the STAT key again.Go to CALCIf you have Linear function go to 4:LinReg(ax+b)Quadratic function go to 5:QuadRegExponential function go to 0:ExpRegFunction for table 1Function for table 2Function for table 3Now. What do you think we should do, when we have graphs instead of tables?228600-317500 Identify at least 5 order pairs from the graph accurately:Organize them in a table and you are back to square one. Follow directions from above. Now it’s your turn434340027813000Mathematician: __________Homework 8-3A) Look at the following tables: Identify if the function is linear, exponential or quadratic and write its function. xy-314-24-1-20-41-224314B) Graph all 3 functions in the coordinate plane: C) Find the average rate of change (slope) over the interval 0 ≤ x ≤ 3 for these functions then put them from least to greatest. NYS CC regent questions:The table below shows the average yearly balance in a savings account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited. Which type of function best models the given data?266700317500 (1) linear function with a negative rate of change(2) linear function with a positive rate of change(3) exponential decay function(4) exponential growth functionNeed simple vs compounded interest rate problemKrystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually. No deposits or withdrawals were made. Which expression can be used to determine how much money Krystal had in the account when she turned 18? (1) 3000(1+0.02)16 (3) 3000(1+0.02)18 (2) 3000(1-0.02)16 (4) 3000(1-0.02)18 ................
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