Alg2+Unit+5

context. function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. **F-BF.2** Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. **F-IF.8**. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. // For example, //identify percent rate of change in functions such as y = (1.02) t, y = (0.97)t, y = (1.01)12t, y = (1.2) t/10, and classify them as representing exponential growth or decay. trigonometric functions, showing period, midline, and amplitude. || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Anchor Standard/Mathematical Practice(s)**=== 1. Make sense of problems and perseveres in solving them. 2. Reasons abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity and repeated reasoning. || Remembering Understanding Applying Analyzing Evaluating Creating || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Learning Target/Task Analysis**===
 * ===**Common Core Standard(s)**===
 * A-SSE.3.** Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.★
 * **c**. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212tto reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
 * A-CED.1.** Create equations and inequalities in one variable and use them to solve problems. //Include equations arising from linear and quadratic functions, and simple rational and exponential functions.//
 * A-CED.2**. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
 * F-BF.1.** Write a function that describes a relationship between two quantities.★
 * a**. Determine an explicit expression, a recursive process, or steps for calculation from a
 * b**. Combine standard function types using arithmetic operations. For example, build a
 * A-SSE.4**. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. //For example, calculate mortgage payments.//★
 * F-LE.3**. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
 * F-LE.4**. For exponential models, express as a logarithm the solution to //ab////ct// = //d// where //a//, //c//, and //d// are numbers and the base //b// is 2, 10, or //e//; evaluate the logarithm using technology.
 * b**. Use the properties of exponents to interpret expressions for exponential functions.
 * F-IF.7.** Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
 * e**. Graph exponential and logarithmic functions, showing intercepts and end behavior, and
 * ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Information Technology Standard**=== || ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Revised Bloom's Level of thinking**===

**I can...**

 * Use properties of exponents to write an exponential function
 * Create equations and inequalities in one variable
 * Determine an explicit expression
 * Determine a recursive process
 * Determine the steps for calculations from the given information
 * Combine standard function types
 * Write arithmetic and geometric sequences
 * Derive and apply the formula of a finite geometric series
 * Compare graphs of linear, quadratic, and exponential functions
 * Express logarithms as solutions to exponential functions using bases 2, 10 and e
 * Use technology to evaluate a logarithm
 * Use properties of exponents to write an exponential function and find the rate of growth or decay
 * Use properties of exponents to interpret rate of change and classify them as growth or decay
 * Graph functions and identify key features by hand or technology
 * Identify intercepts, maximums and minimums of functions
 * Identify and graph square root, cube root, piecewise, exponential, logarithmic, trigonometric and absolute value functions
 * <span style="font-family: 'Tahoma','sans-serif'; font-size: 11px;">Identify zeros and end behaviors by graphing functions

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍===

**Essential Vocabulary**
exponentially, base, logarithm, trigonometric functions, midline, amplitude, finite geometric series

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Sample Assessments**=== ===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Differentiation**===

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Instructional Resources**===

===‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍‍**Notes and Additional Information**===