Learning Resource Type

Classroom Resource

The Exponential Function Video

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This video from MIT Open CourseWare on the CK-12 website will explore the meaning of exponential growth or decay by solving a differential equation that models such growth or decay.

    Mathematics (2019) Grade(s): 09-12 - Precalculus

    MA19.PRE.24

    Compare and contrast families of functions and their representations algebraically, graphically, numerically, and verbally in terms of their key features. Note: Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; maximums and minimums; symmetries (including even and odd); end behavior; asymptotes; and periodicity. Families of functions include but are not limited to linear, quadratic, polynomial, exponential, logarithmic, absolute value, radical, rational, piecewise, trigonometric, and their inverses.

    Unpacked Content

    UP:MA19.PRE.24

    Vocabulary

    • Function
    • Relative Maximum
    • Relative Minimum
    • Symmetry (Even/Odd)
    • End Behavior
    • Asymptotes
    • Intercepts
    • Increasing/Decreasing Intervals
    • Periodicity
    • Absolute Maximum
    • Absolute Minimum

    Knowledge

    Students know:
    • Properties of functions and make connections between different representations of the same function

    Skills

    Students are able to:
    • Compare properties of functions when represented in different ways (algebraically, graphically, numerically in tables or by verbal descriptions).

    Understanding

    Students understand that:
    • Each representation provides a unique perspective of the function.
    • Different representations are most appropriate for revealing certain key features of the function
    Mathematics (2019) Grade(s): 09-12 - Precalculus

    MA19.PRE.25

    Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Extend from polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.

    Unpacked Content

    UP:MA19.PRE.25

    Vocabulary

    • Average rate of change
    • Specified interval
    • Difference Quotient

    Knowledge

    Students know:
    • Techniques for graphing.
    • Techniques for finding a rate of change over an interval on a table or graph.
    • Techniques for estimating a rate of change over an interval on a graph.

    Skills

    Students are able to:
    • Calculate average rate of change on a specified interval when given an equation or table ofa polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions.
    • Interpret the average rate of change of a polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions in the context of a problem when given symbolic representations, tables, graphs, or contextual situations.
    • Estimate the average rate of change for a specific interval of a polynomial, exponential, logarithmic, and radical to rational and all trigonometric functions functions when given agraph.

    Understanding

    Students understand that:
    • The rate of change is the ratio of the change between the dependent and independent variable.
    Link to Resource

    Resource Provider

    Other

    Resource Provider other

    CK-12
    Accessibility
    License

    License Type

    CUSTOM
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