CR March 3

College Readiness
- Unit 6 - Exponential
Functions

By Mr. Pousada

Devices

Please put aware all phones,
earpods, other electronic devices
(ipads etc…) and focus for
instruction. Thank you!

Standards

A.SSE.1: Interpret expressions that represent a quantity in terms of its context.

A.SSE.1a: Interpret parts of an expression, such as terms, factors and coefficients, in context.

A.SSE.1b: Given situations which utilize formulas or expressions with multiple terms and/or factors, interpret the meaning (in context) of individual terms or factors.

A.SSE.2: Use the structure of an expression to rewrite it in different equivalent forms. For example, see x4 – y4 as (x2 ) 2 – (y2 ) 2 , thus recognizing it as a difference of
squares that can be factored as (x2 – y2 )(x2 + y2 ).

A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.3a: Factor any quadratic expression to reveal the zeros of the function defined by the expression.

A.SSE.3b:Complete the square in a quadratic expression to reveal the maximum or minimum value of the function defined by the expression.

A.CED.2: Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes
with labels and scales. (The phrase “in two or more variables” refers to formulas like the compound interest formula, in which A = P (1 + r/n)nt has multiple variables.)

A.CED.4: Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations. Examples: Rearrange Ohm’s law V = IR to highlight
resistance R; Rearrange area of a circle formula A = πr2 to highlight the radius.

F.IF.4: Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph
showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end
behavior; and periodicity.

F.IF.7: Graph functions expressed algebraically and show key features of the graph both by hand and by using technology.

F.IF.7e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline and amplitude.

Standards

F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8b: Use the properties of exponents to interpret expressions for exponential functions. 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 and decay.

F.BF.1: Write a function that describes a relationship between two quantities.

F.BF.1a: Determine an explicit expression and recursive process (steps for calculation) from context. For example, if Jimmy starts out with $15 and earns $2 a day, the
explicit expression “2x + 15” can be described recursively (either in writing or verbally) as “to find out how much money Jimmy will have tomorrow, you add $2 to his total
today.” Jn = Jn-1 + 2, J0 = 15.

F.BF.2: Write arithmetic and geometric sequences recursively and explicitly, use them to model situations, and translate between the two forms. Connect arithmetic
sequences to linear functions and geometric sequences to exponential functions.

F.LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.1a: Show that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. (This can be
shown by algebraic proof, with a table showing differences or by calculating average rates of change over equal intervals.) F.LE.1b:Recognize situations in which one
quantity changes at a constant rate per unit interval relative to another. F.LE.1c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit
interval relative to another.

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).

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. Interpret expressions for functions in terms of the situation they model.

F.LE.5: Interpret the parameters in a linear (f(x) = mx + b) and exponential (f(x) = a•dx ) function in terms of context. (In the functions above, “m” and “b” are the parameters
of the linear function, and “a” and “d” are the parameters of the exponential function.) In context, students should describe what these parameters mean in terms of change
and starting value.

Essential Questions

●Why might two expressions look different but be mathematically the same?

●Why might someone want to change the way an expression is written?

●How would you know that two expressions are mathematically equivalent?

●When might real life financial situations be modeled with math? Why would some debts be
considered good or bad?

●Why will it matter how interest is compounded on borrowed money?

●When would financial situations follow an exponential growth or decay and how would you
determine if it is exponential growth or decay?

●How would you apply the concept of sequences to different types of debt?

Vocabulary

compounded interest, continuously compounded, daily, depreciation, interest, periodically
compounded, quarterly, radical, rational exponent, semiannually, weekly,

Review and Remediation

Please go to Canvas, then assignments, then click on CR March 3 Deltamath

Draw

Draw an exponential equation that has a y intercept of 3 and factor of 2: