Standards Map

Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Seeing Structure in Expressions

Cluster - Write expressions in equivalent forms to solve problems.

[AI.A-SSE.B.3.c] - Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

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Resources:

• Exponent
  The number that indicates how many times the base is used as a factor, e.g., in 4³ = 4 x 4 x 4 = 64, the exponent is 3, indicating that 4 is repeated as a factor three times.
• Exponential function
  A function of the form y = a •b^x where a > 0 and either 0 < b < 1 or b > 1. The variables do not have to be x and y. For example, A = 3.2 • (1.02)^t is an exponential function.
• Expression
  A mathematical phrase that combines operations, numbers, and/or variables (e.g., 3² ÷ a).

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Predecessor Standards:

• 7.RP.A.3
  Use proportional relationships to solve multi-step ratio, rate, and percent problems. For example: simple interest, tax, price increases and discounts, gratuities and commissions, fees, percent increase and decrease, percent error.
• 7.EE.A.1
  Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x +1) and -3(x – 5/3) = -3x + 5.
• 8.F.A.3
  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
• 8.F.B.4
  Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

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Successor Standards:

No Successor Standards found.

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Same Level Standards:

• AI.N-RN.A.2
  Rewrite expressions involving radicals and rational exponents using the properties of exponents.
• AI.A-SSE.A.2
  Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)² – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2 ) – 3).
• AI.F-IF.C.8.b
  Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as identifying appreciation and depreciation rate for the value of a house or car some time after its initial purchase: V_n=P(1+r)ⁿ. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, and y = (1.2)^{t /10}, and classify them as representing exponential growth or decay.