a Graph the points to compare it to the family of functions you know, and see which fits best.
B
b According to the graph from Part A, what sequence would this relationship represent best?
A
a It belongs to the family of exponential functions. See solution.
B
b It describes a geometric sequence. See solution.
Practice makes perfect
a We are given the data recorded when dropping a ball from different heights. We need to find what family the function belongs to and explain our reasoning.
Let's start by plotting the points and seeing to what family of functions the given relation looks similar to.
As we can see, the behavior of the relationship between the rebound height and the bounce number is better described by an exponential function.
b Now, we will think about the data of Part A as a sequence. Notice that in Part A we saw that it is very close to be an exponential function. If this is true, this means that each term can be found by multiplying the previous term by a constant number, making it a geometric sequence. Let's check.
Notice that the multiplier is not constant, but it is very close from term to term. This is because the measurements cannot be done with total precision. This behavior would only follow a geometric series perfectly in an ideal case. Nevertheless, a geometric sequence still describes it better than the other sequences.
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