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Mathematics > Course Model Mathematics I (Integrated Pathway) > Linear, Quadratic, and Exponential Models
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Mathematics | Course : Model Mathematics I (Integrated Pathway)

Domain - Linear, Quadratic, and Exponential Models

Cluster - Construct and compare linear and exponential models and solve problems.

[MI.F-LE.A.1.a] - Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.*

Resources:


  • Exponential function
    A function of the form y = a •bx 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.
  • Linear function
    A function with an equation of the form y = mx + b, where m and b are constants

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.
  • 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.
  • 8.F.B.5
    Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MI.F-BF.A.2
    Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.*
  • MI.F-LE.A.1.b
    Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.*
  • MI.F-LE.A.1.c
    Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.*
  • MII.F-IF.C.8.b
    Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as Identifying appreciation/depreciation rate for the value of a house or car some time after its initial purchase: Vn=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.