The Exponential Function Video

Learning Resource Type

Classroom Resource

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.

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.

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.

Resource Provider

Other

License Type

CUSTOM

Resource Provider other

CK-12
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