Last week we did a couple of open-ended practice task problems. Monday (if we don't get another foot of snow!), you will complete an open response problem that is probably less difficult than the practice problems we did together, but will still challenge you to make sense of a problem and apply what we have learned to solve problems pertaining to volume in a different context. This will count as the first test grade of the new quarter. I don't think most of us really need to do a whole lot of studying for this task, but if you want to spend 10 minutes preparing, it would be a good idea to organize your unit 4 polynomial notes and perhaps log on to www.khanacademy.org and search "Dimensions from volume of box". There is a short 5-minute video that shows a simpler problem than what you will need to complete, but the core problem solving elements are pretty similar and it should build your confidence.
Guiding Questions for Tenmarks Problems
To prepare for upcoming material, your weekend homework was to complete 4 www.tenmarks.com tracks to refresh your memory about the key features and behavior of exponential graphs, structure of exponential equations, and patterns to interpret tables of values modeling exponential functions.
Your first homework grade will be your TM scores for the four assigned tracks. One student finished all four last Monday in about 30 minutes. I recommend your complete the tracks and as you are working, answer the following guiding questions:
Your first homework grade will be your TM scores for the four assigned tracks. One student finished all four last Monday in about 30 minutes. I recommend your complete the tracks and as you are working, answer the following guiding questions:
- Representing and Interpreting Exponential Functions [FIF7e] . For polynomial functions we learned about key features and behavior of that family of function. Given a simple exponential function y = b^x, what key features do we need to recognize? What is different about the behavior and rates of change of an exponential function compered to other functions we have studied.
- Understanding Exponential Growth and Decay [F-IF.8b] For polynomial functions, we learned what how each of the parameters in y = a (x-h)^3 +k affects the graph of a polynomial. What can you recognize about the roles of the a and b for a polynomial function y = ab^x? What happens if b>1? What happens when 0<b<1?
- Calculating Exponential Growth and Decay Algebraically [F-LE.1c] For linear functions, we know all about positive and negative slope and the y-intercept for any y = mx+b. Exponentials are not characterized by slope and the y-intercept is not a "b". What can you generalize about the y-intercept of exponential functions? What is generally true about the x-intercept(s)?
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