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Newton's Law of Cooling
Your Algebra learners analyze and solve an exponential equation in this popular, real-life model of the cooling of a liquid.
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Linear or Exponential?
Your learners analyze various real-life contexts to decide if each is a linear or exponential model. This could be used as an assessment of learners' skills of discerning between a linear and an exponential model.
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Vernier EasyData App
Used along with data collection devices, the EasyData Application for the TI-83 Plus/TI-84 calculator allows learners to use real data to learn math and science. Statistics, curve fits, and integrals are used to analyze the collected...
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Interesting Interest Rates
Your young bankers compare earning interest accumulated yearly and monthly to decide which method most increases their balance. Using an exponential function to model the bank balance affords the learners more practice connecting these...
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Illegal Fish
Your young fishermen learn about exponential function growth by interpreting the pieces of the given equation within the context of numbers of fish in a lake.
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Exponential Growth Versus Linear Growth I
Your algebra learners will discover how quickly an exponential function value grows compared to a linear function's value. Making a table of values helps in this comparison, set in the context of making a wage for raking leaves.
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A Saturating Exponential
Your learners analyze the familiar model of a cold beverage warming when it is taken out of the refrigerator. The general form of the equation and its graph are presented. Learners learn about the specific pieces of the function by...
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Exponential Growth versus Polynomial Growth
Your algebra learners explore the values of two types of functions in order to compare growth rates in this short cooperative task. Two types of solutions are given, using a table of values and an abstract argument.
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Exponential Growth versus Linear Growth II
Your algebra learners discover that exponential functions, with a base larger than one, outgrow linear functions when the inputs increase sufficiently. Their analysis includes using a graphing calculator to produce tables.
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Exponential Functions
Your algebra learners analyze and interpret the general form and the graph of two functions. The increase of the function due to the multiplicative factor is emphasized.
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Bacteria Populations
Your young microbiologists will interpret and solve exponential equations in this real-world context task set in a hospital research scenario. Learners think in terms of the functions as well as their rates of change.
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Your Father
Your learners will explore the idea that not all functions have real numbers as domain and range values as seen in this real-life context. Secondly, the characteristics required for a function to have an inverse are explored including...
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Find Parabolas through Two Points
Your learners will write quadratic functions whose graphs include specific points and explore how these graphs are related to each other.
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The Customers
Exploring functions not represented by an expression is this task's secret. As your learners organize business customers in a database, they explore the definition of what it is to be a function.
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Domains
Your algebra learners work to address the order of operations applied to an expression's input variable and the limitations that may be created because of it. This simple task of a few very well-chosen exercises is elegant in it's way of...
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Cell Phones
Your texters will enjoy assessing their knowledge of function notation in this simple set of exercises. They will also interpret function notation in terms of the given context.
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Algae Blooms
Your microbiologists explore a changing algae population and build an exponential function modeling algae concentration from the description given of the relationship between concentrations in cells/ml and days of rapid growth.
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US Households
Learners construct and use inverse functions to model a real-world context. They use the inverse function to interpolate a data point.
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A Valuable Quarter
Your young bankers model an account balance with an exponential function and solve the equation by extracting a root or taking a logarithm. The task involves the context of annual and compounding interest as well as some interesting...
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Skeleton Tower
Your algebra learners build a quadratic function in this task of counting the blocks used to build objects. The arithmetic sequence that shows up brings up a shortcut to the long addition using the Gauss Method. Eventually, learners...
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Model Air Plane Acrobatics
Your young airplane enthusiasts will enjoy this collaborative task of graphing an airplane's distance from the ground as it flies in a perfect circle. They will discover that they have graphed a sinusoidal function that comes from the...
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Latitude
Your young geologists generate a graph given a table of values from the context of latitude and percent of the earth's surface north of that latitude. The questions in the activity then focus the learners to a deeper understanding of the...
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Temperature Conversions
Your young weather buffs use compositions and inverses of functions to convert between Celsius, Fahrenheit, and Kelvin degrees. Then they analyze possible compositions and whether they exist in the real-life context.
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Summer Intern
Your young apprentices build a function describing the percent concentration of salt in a brine. The rational function is then related to the parent function, y= 1/x, and graphed. Finally, the apprentices predict the amount of fresh...