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Algebra 1

5.3.3 Compare and Contrast Two Patterns

Algebra 15.3.3 Compare and Contrast Two Patterns

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Activity

Here are graphs showing how the amount of money in each of the purses change. Remember, Purse A starts with $1,000 and grows by $200 each day. Purse B starts with $0.01 and doubles each day.

Scatter plot showing amount in dollars (y-axis) versus number of days (x-axis). Blue and red dots represent data points, with blue points increasing rapidly after 20 days. Points Q is labeled on day 5 and P is labeled on day 9.

1. Which data on the graph shows the amount of money in Purse AA? Which data on the graph shows the amount of money in Purse BB? Explain how you know.

2. Points PP and QQ are labeled on the graph. Explain what they mean in terms of the genie’s offer.

3. What are the coordinates of the vertical intercept for each graph? Explain how you know.

4. When does Purse B become a better choice than Purse A? Be prepared to show your reasoning.

5. Knowing what you know now, which purse would you choose? Be prepared to show your reasoning.

While on a beach, your friend discovers a different genie. This genie also offers two purses to choose from, and he gives you the following graph to show how the money in each purse will grow. The set of triangular marks that lie on a line represent values in Purse A, and the set of square marks that make a curve represent those in Purse B.

Line graph comparing the growth of two purses, A (red squares) and B (blue triangles), in dollars over 15 days. Purse B increases faster, surpassing Purse A after day 10. Y-axis ranges from 0 to 4,500 dollars.

6. The genie is still deciding how many days he will let the money in the purses grow. Help your friend plan a strategy for picking the purse with more money while the genie thinks.

Are you ready for more?

Extending Your Thinking

“Okay, okay,” the genie smiles, disappointed. “I will give you an even more enticing deal.” He explains that Purse B stays the same, but Purse A now increases by $250,000 every day. Which purse should you choose?

Self Check

The graph shows the yearly balance, in dollars, in two investment accounts. Account A starts with $2,000. Account B starts with $1,000.

  1. Both accounts grow by the same amount each year.
  2. Both accounts grow more quickly as time goes on.
  3. Account A grows by the same amount each year. Account B grows more quickly as time goes on
  4. Account A grows more quickly as time goes on. Account B grows by the same amount each year.
Scatter plot with two data sets: blue and red dots. Both show increasing amounts in dollars over 14 years, with the red dots consistently higher than the blue until year 10 when the curve of the blue line raises above the linear red line.

Additional Resources

Compare and Contrast Graphs

Compare and contrast the graphs of y=2xy=2x and y=2xy=2x.

To compare and contrast the graphs of these functions, you would first need to graph them.

Graph of a line that passes through the origin and the points (1, 2) and (negative 1, negative 2).
xx y=2xy=2x
–1 –2
0 0
1 2
2 4
Graph of ( y = 2 x ) ( y = 2 x )
A graph of the exponential function y = e^x, showing a curve passing through (0,1) and rising steeply for positive x-values, with the y-axis as the line of growth. The x-axis ranges from -4 to 5, and the y-axis from -5 to 5.
xx y=2xy=2x
–1 1212
0 1
1 2
2 4
Graph of ( y = 2 x ) ( y = 2 x )

Both equations have a 2 and an xx in them, but in y=2xy=2x, xx is multiplied by 2, and in y=2xy=2x, 2 is the base and xx is the exponent. If you graph the equations together on the same grid, it makes it easier to discuss the key features and compare the graphs.

Graph of the line y equals 2x and graph of the exponential function y equals 2 to the x power, intersecting at the points (1, 2) and (2, 4).
  • The graphs intersect at (1,2)(1,2) and (2,4)(2,4).
  • y=2xy=2x has a yy-intercept of (0,0)(0,0). y=ß2xy=ß2x has a yy-intercept of (0,1)(0,1).
  • When 1<x<21<x<2, y=2xy=2x is greater than y=2xy=2x.

Try it

Try It: Compare and Contrast Graphs

Compare and contrast the graphs of y=3x+1y=3x+1 and y=3xy=3x.

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