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Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability
Display Title
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability
What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis.
Exponential Functions
Brief Review of Exponents
When a number is raised to a power, exponents are involved. Here are the key components of an exponential expression.
Exponents make it easier to write expressions that would otherwise be cumbersome to write. See how much easier it is to write 3^{10} instead of the expression on the right?
Exponents are a different form of writing numbers. With this new form come new properties that are unique to exponents. The next section goes over these properties, also known as the Laws of Exponents.
Laws of Exponents
The Laws of Exponents are a set of properties that pertain to all exponential expressions. Study the definition below.
To learn more about exponents, click on this link. It is a presentation that goes over the Laws of Exponents in more detail. To see examples that use the Laws of Exponents, click on this link.

Exponential Functions
An exponential function is of this form:
In this function the terms a, b, and c are numbers and x is the independent variable. Here’s one of the simplest exponential functions:
This is the graph of the function.
As you can see from the graph, the values of f(x) increase dramatically for small increases in input values of x. Here are some other examples of exponential functions.






Compound Interest
A special case involving exponential expressions is compound interest. What is compound interest? Usually, the context is of money earning interest in a bank account.
Here is the compound interest formula
This is the formula to use when the compounding periods are noncontinuous. Use this formula for continuous compounding:
To see examples of calculating compound interest, click on this link.

This is part of a collection of closed captioned videos for the Algebra Nspirations video series. To see the complete collection of the videos, click on this link.
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Common Core Standards  CCSS.MATH.CONTENT.6.SP.B.5, CCSS.MATH.CONTENT.8.SP.A.1, CCSS.MATH.CONTENT.HSS.CP.A.1, CCSS.MATH.CONTENT.HSS.CP.A.2, CCSS.MATH.CONTENT.HSS.CP.A.3, CCSS.MATH.CONTENT.HSS.CP.A.4, CCSS.MATH.CONTENT.HSS.CP.A.5, CCSS.MATH.CONTENT.HSS.CP.B.6, CCSS.MATH.CONTENT.HSS.CP.B.7, CCSS.MATH.CONTENT.HSS.CP.B.8, CCSS.MATH.CONTENT.HSS.CP.B.9 

Duration  33 minutes 
Grade Range  6  9 
Curriculum Nodes 
Algebra • Probability and Data Analysis • Data Analysis • Data Gathering 
Copyright Year  2020 
Keywords  algebra, data analysis, probability, statistics, Closed Captioned Video 