Wednesday, January 08, 2025

Exponential Functions – What You Need to Know

Exponential models are useful in a number of real-world scenarios, from predicting declines in population to forecasting growth in asset values. This can all get rather complicated, and both the SAT and ACT require some familiarity with exponential functions. 

Fortunately, only knowledge of bare basics is required. 

Following is a list of things you need to know about exponential functions. 

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Simple definition
Exponential functions have an unknown in the exponent.

Exponential functions – general form
y = A*B^x.
x is usually time, t.

Constants
A is the “initial value” (y when x=0).
B is the “multiplier.”

Growth factor
B = (1±r), where r is rate of growth/decay.
(Time and rate units must match).

Parent Graph
Rising curve through (0,A).
Horizontal asymptote y = 0.

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For practice, search Google for worksheets covering any or all of the above, pick a worksheet that provides answers, complete the worksheet, analyze any mistakes, and redo it until you can complete that worksheet with no errors. Then repeat, with additional worksheets, as needed, until you’ve mastered this material.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, January 01, 2025

Essential Ti-84 Plus CE Skills

Texas Instrument’s handheld Ti-84 Plus CE graphing calculator is a powerful math computer, the best available calculator for use on the ACT (a different  graphing calculator, Desmos, is featured in the BlueBook app used to take the SAT).

Clever use of the Ti-84 Plus CE can make significantly improve scores on the ACT math test. Unfortunately, the calculator is as complicated as it is powerful, with hundreds of features and functions. Shortening the list is critical.

Which calculator skills are most important?

Click here for my outline of essential Ti-84 Plus CE skills. Students are encouraged to do independent study using targeted Google searches to learn and practice any underdeveloped skills listed in the linked document above.

Graphing calculators like the Ti-84 Plus CE have played an important role in teaching and learning mathematics for decades, and as of this writing, this calculator is still standard technology in high and college mathematics courses.

Mastering the Ti-84 Plus CE beyond beginning levels confers multiple benefits, and is highly recommended.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.