Exploring Exponential Growth and Decay Graphs
Exploring Exponential Growth and Decay Graphs
Investigate exponential functions by adjusting key parameters. Observe how base values greater or less than 1 change the graph’s shape.
Putting It All Together
Answer these open ended questions on your own or with others to form deeper math connections.
Open-ended question 1
Draw the function . What are the coordinates of point ? What are the coordinates of point ? Are the positions of points and unique, or is it possible to obtain the same graph by assigning different coordinates to these points?
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Open-ended question 2
Place point at , then move point to . Compare the coordinates of with the equation of the exponential function. What do you notice? Does this relationship hold for any position of point in the plane, or only when the -coordinate of is ? Justify your answer, providing a counterexample if appropriate.
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Open-ended question 3
Consider the function . Does this function represent an exponential growth or decay model? Can you rewrite this function using the form ? If so, what are the values of and ?
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Open-ended question 4
The mathematician in you feels creative today. You want to create an exponential decay model with a starting value of 1.56. What could a possible equation for this model be?
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