Students determine that the inverse of the exponential function is the natural log function by plotting the inverse of exponential solution points.
Students will find an approximation for the value of the mathematical constant e and to apply it to exponential growth and decay problems.
Arithmetic Sequences & Series
Students use formulas to find the differences of the consecutive terms, plot a scatter plot of each sequence, and determine that sequences with common differences (called arithmetic sequences) have scatter plots whose points form a straight line.
Students graph data modeling exponential and logarithmic growth and find equations representing the data.
Change Of Base
Discover the change of base rule for logarithms by examining the ratio of two logarithmic functions with different bases.
Constructing an Ellipse
Students explore two different methods for constructing an ellipse.
Geometric Sequences & Series
Students find common ratios of geometric sequences on a spreadsheet and create scatter plots of the sequences to see how each curve is related to the value of the common ratio and/or the sign of the first term of the sequence.
Properties of Logarithms
Students use a combination of algebra and graphing to discover the properties of logarithms.
Students use the sequence mode of the graphing calculator to generate recursive sequences and then examine the values.
Students use the calculator to create an arithmetic sequence and explore the effect of each variable in the formula of the nth term of an arithmetic sequence.
Sums of Sequences
Students develop formulas for the sum of arithmetic and geometric sequences and then find the sum of sequences using the formulas developed.
Domain & Range
Students explore a variety of mathematical functions and real world applications of functions to understand the concepts of domain and range.