1. Describe an exponential growth pattern. Include key properties such as growth factors.
Definition in the GGG Exponential Functions book- Exponential growth: A pattern of increase in which each value is found by multiplying the previous value by a constant factor greater than 1.
My definition- Exponential growth: What the book is basically trying to say is that exponential growth is a pattern where the value is multiplied by a constant number to get to the next value, whether it's filling out a table, or plotting a graph, or can use this information. The constant number is called the growth factor, and is multiplied to the value to get the next value. This relationship is called an exponential function. As a rule, the independent variable increases/decreases by a constants amount, while the dependent variable doesn't.
Example:
In this table you can see that the x value has a constant rate of change and increases by the same amount every next student. But on the other hand the money made keeps increasing by more and more. Every amount multiplied by 2 equals the next amount of money made on the table. The exponential growth/pattern in this case would be 1, 2, 4, 8, 16... this shows exponential growth in which each value is 2 times the previous value.
2. How are exponential functions similar to and different from the linear functions you worked with in earlier units?
Linear functions:
- Have a constant rate of change.
- So basically the y and x axis's need to increase by the same amount each time.
- The x axis can't be the only axis increasing by the same amount, as the y axis's amount keeps increasing and increasing.
Similar:
- Both functions increase or decrease by a certain rate. But different in many ways too.
Exponential Functions:
- The x axis increases/decreases by a constant rate, so either by 1's, 2's, 3's, 40's, anything really. As long as it's constant.
- The y axis increases/decreases too, but it's not constant. The amount between values keep increasing by double, triple, quadruple, anything really.
- Different from linear function as both x and y axis's in a linear function increase constantly, while here only x axis does, and y axis increases by more and more each time.
Definition in the GGG Exponential Functions book- Exponential growth: A pattern of increase in which each value is found by multiplying the previous value by a constant factor greater than 1.
My definition- Exponential growth: What the book is basically trying to say is that exponential growth is a pattern where the value is multiplied by a constant number to get to the next value, whether it's filling out a table, or plotting a graph, or can use this information. The constant number is called the growth factor, and is multiplied to the value to get the next value. This relationship is called an exponential function. As a rule, the independent variable increases/decreases by a constants amount, while the dependent variable doesn't.
Example:
2. How are exponential functions similar to and different from the linear functions you worked with in earlier units?
Linear functions:
- Have a constant rate of change.
- So basically the y and x axis's need to increase by the same amount each time.
- The x axis can't be the only axis increasing by the same amount, as the y axis's amount keeps increasing and increasing.
Similar:
- Both functions increase or decrease by a certain rate. But different in many ways too.
Exponential Functions:
- The x axis increases/decreases by a constant rate, so either by 1's, 2's, 3's, 40's, anything really. As long as it's constant.
- The y axis increases/decreases too, but it's not constant. The amount between values keep increasing by double, triple, quadruple, anything really.
- Different from linear function as both x and y axis's in a linear function increase constantly, while here only x axis does, and y axis increases by more and more each time.
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