1. Describe an exponential growth pattern. Include key properties such as growth factors.
- An exponential growth pattern is a pattern that increases when each value multiplies the previous value by a factor that stays constant. The value must be greater than 1. One example is in the ballots problem that we were assigned to do for homework. Each value in the problem went up in a sequence: 2, 4, 8,16, 32 and so on. As the number of cuts increases by 1, the number of doubles or multiplies by 2. The growth factor is the constant value that each number is multiplied by the get the next one. In this situation, this means that the growth factor is 2. If you were to graph an exponential growth pattern, it would look like an inverse variation pattern, however it would be opposite. Both the x and y values increase, which is not like inverse variation. But both of the patterns do not have a constant rate of change like a linear relationship would. Looking at an exponential growth pattern on a graph, the pattern would increase slowly at first, then faster and more rapidly. As a result, a curve is shown on the graph.
2. How are exponential functions similar to and different from the linear functions you worked with in earlier units?
- Exponential functions are very different, however there are still similarities. Both have a particular pattern that is followed and used to find the next values in the sequence. But linear functions have a constant rate of change: on a graph the line would be straight, and the points on the line would increase or decrease at the same rate each time. However for exponential functions, the rate of change is not constant. It increases slowly in the beginning, then rapidly. Linear functions increase/decrease byusing addition or subtraction, but exponential functions increase by using multiplication
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