Does linear growth have to add the exact same amount, so a constant amount, each time or does it just have to be close?
Linear growth refers to a consistent increase in a quantity over time. In the context of your question, linear growth does not necessarily have to add the exact same amount every time; it can vary as long as the change remains proportional.
To determine if a growth pattern is linear, you can examine the difference between consecutive values. If the difference remains approximately constant or varies linearly, then it can be considered linear growth.
Let's take an example to understand this better. Suppose you have a sequence of numbers: 2, 5, 8, 11, 14, 17. To determine if these numbers exhibit linear growth, we can calculate the differences between consecutive terms: 5-2=3, 8-5=3, 11-8=3, 14-11=3, 17-14=3. Here, we can see that the differences (3 in this case) remain constant, indicating linear growth.
However, if we had a sequence like 2, 5, 7, 10, 13, 15, we can calculate the differences: 5-2=3, 7-5=2, 10-7=3, 13-10=3, 15-13=2. In this case, the differences are not constant, indicating that it is not linear growth.
Therefore, it is not necessary for linear growth to add the exact same amount each time, but the changes should be proportional or remain approximately constant.