GGG Mathematical Reflections 1

1. Describe an exponential growth pattern. Include key properties such as growth factors.

An exponential growth pattern is when one value is multiplied by a common factor to get a new value, or number. For example, each time x increases by 1, the previous y value is multiplied by this constant factor to get a new value for x. In an exponential function, the constant factor is also the growth factor. An example of an exponential growth pattern is when you have 3 to the power of n. For this, the pattern would be would look something like this: 3, 9, 27, 81, 243, and so on. This is an exponential growth pattern because each time x increases by 1, y variable is multiplied by 3 to get to the next value.

2. How are exponential functions similar and different from the linear functions you worked with in earlier Units?

Linear and exponential functions are similar because they both increase or decrease in a specific pattern on a graph or table. A difference between both functions is that exponential functions on a graph is not linear, but instead it goes in an upward curve that goes steeper as it goes higher. On the other hand, a linear function on a graph would be a straight line since the slope is always constant. Also, exponential functions always include exponents, while linear functions never do.