Algebra I STAAR 2022: Question 44: Matching Exponential Function Equations to a Given Table

In this video, I will use my TI-Nspire calculator to find which exponential function best models the data shown in a table. Remember: the BEST does not always mean PERFECT!

How should you study? Watch the videos, follow along with me using your calculator, copy the notes at the end.

[joseph_donovan]

Thank you for this insightful video Miss. I like the way you make a connection between exponential functions and tables, and how the TI nSpire can add clarity to my understanding.👌

[Tovarris]

I enjoyed the video, but this problem does not need a calculator, nor should it require as much time or math. The easiest way to solve this problem is to solve by process of elimination. It is obvious upon reading the answer choices that each equation is expressed in the form r(x) = a(r)^x, an exponential equation. This fact, in combination with the realization that as x increases, r(x) increases as well should be enough to eliminate answer choice H, as with a value for r of less than 1, r(x) will decrease as x increases due to the fact that a number less than 1 will always decrease when put to a positive power. Another observation that can be made is that although the increase is exponential, r(x) is not increasing by an obsurdly large amount with every increase of x within the range of the table. Due to the nature of exponential equatios, this should rule out answers G and J, as having an r value as big as 200+ would increase the value of r(x) by a factor of over 8, 000, 000, or 200^3, for everytime that x increases by 3. This is not shown by the table, as the increase between any two adjacent x values in the table is never more than a factor of even 2. Thus, answer choice F is correct as it is the only remaining answer choice.
Although teaching the solution to this problem in the way you did is technically an easier method, blindly inputting numbers and equations into a calculator does not require the understanding of exponential equations and how they work, which is critical for future math classes such as Algebra II and beyond. In addition, spending too much time on simpler problems like this may slow one down in other future exams like the SAT, where time management is so crutial. At the very least, some effort should be put into eliminating answer choices before using a calculator. I did still enjoy the video and the Spanish translations, however I don't fully agree with the methods used.

[naderhumood]

Thank you v much. Video is great, how would I expand an expresion in the same cal CX, many thanks.