So far in this chapter you have looked at several types of sequences and compared linear and exponential growth patterns in situations, tables, and graphs.

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Presentation transcript:

So far in this chapter you have looked at several types of sequences and compared linear and exponential growth patterns in situations, tables, and graphs. In this lesson you will compare patterns of growth rates to each other. This work will also help you write equations for exponential sequences in the next lesson.

5-82. PATTERNS OF GROWTH Your Task: Represent these three sequences on a graph. Use a different color for each sequence. Although the graph is discrete, connect the points so you can see the patterns more easily. Discussion Points How do the inputs, n, and the outputs, t(n), of each sequence increase? How does the sequence grow? Is the rate of change constant or changing? How? (Make growth triangles to help answer this question.) If you knew a specific term, how would you find the next term? For example, if you knew the 10th term, could you find the 11th term? Which family of functions best models each sequence?

Would your answer change if you kept the account for many years? 5-83. GROWTH RATES IN SEQUENCES Consider how fast each of the sequences is growing by looking at the tables and the graph. Do not make any additional computations. Instead make conjectures based on the tables and graphs. If n represents the number of years, and t(n) represents the amount of money in your savings account, which account would you want, Sequence A, B, or C? Would your answer change if you kept the account for many years? Obtain the Lesson 5.3.1B Resource Page from your teacher. Extend the tables and the graph to n = 7. The table for Sequence B has been completed for you. Based on your new graph, do you want to change your answer to part (b)? Why or why not?

5-84. WHICH GROWS THE MOST? Will an exponentially growing bank account eventually contain more money than a linearly growing bank account for the same amount of initial savings, no matter how fast (steep) the rate of growth of the linear account? Use the slope triangles on your graph from problem 5-83 to help you explain. How does the growth of a quadratic sequence like Sequence B compare to exponential growth?