Mathematical+Reflections,+p+16

November 29, 2008 M.P.  Big Idea: The rate at which many things grow or decay can often be described mathematically. Essential Question: How can I describe a pattern of repeated multiplication? 1. Based on your work in this investigation, what do you think are the key properties of exponential growth patterns? How are exponential growth patterns different from the linear patterns you have worked on in earlier unit? ** I think that the key properties of exponential growth patterns are the exponent and the base. Exponential patterns are non linear, they are very different from linear equations, equations, and graphs. 2. Consider the exponential equation y = 2x. ** Exponent, and then multiply its base (2) by that many times. Example: y = 23 then in standard form it would look like this 2 x 2 x 2 ** B. Describe the graph of y = 2x**. The graph of the equation y = 2x would be non-linear and the change of rate, slope, would be double of the last number. 3. Consider the exponential equation y = 3x. ** The method is the same as in 2a, the only difference in y=3x is 3. So the base is 3 not 2. The table is the different, y = 3x is tripling and y = 2x is doubling. Example:
 * A. How can you calculate the value of y for a given value of x? **
 * A. How is the method of calculating a y value for a given x value for y = 3x similar to calculating a y value for a given x value for y = 2x? How is it different? **
 * B. How is this table of values for y = 3x similar to a table of values for y = 2x. How is it different? **
 * Exponet || y = 2x || y = 3x ||
 * 0 || 0 || 0 ||
 * 1 || 1 || 1 ||
 * 2 || 2 || 3 ||
 * 3 || 4 || 9 ||
 * 4 || 8 || 27 ||

The graph of y = 3x and y = 2x are similar, both graphs are non-linear and both have very steep slopes. The only difference is the values of y = 3x and that graph will be a little steeper than y = 2x. **Summary**: In this investigation I learned more about exponents. I also learned about exponential growth and patterns
 * C. How is the graph of y = 3x similar to the graph of y = 2x? How is it different? **