Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
3. Function Notation
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Exercise 31 Page 126

How might the number of people with cell phones change from year to year?

No, see solution.

Practice makes perfect
In this case, x and P(x) are the input and output, respectively. Moreover, P(x+1) is the output for x+1. Recall that x represents the number of years after 1990. Let's take a look at the different cases where P(x) is less than, equal to, or greater than P(x+1).
  1. P(x+1)>P(x). Here, the number of people with cell phones x+1 years after 1990 is greater than the number of people with cell phones x years after 1990.
  2. P(x+1)=P(x). Here, the number of people with cell phones x+1 years and x years after 1990 are the same.
  3. P(x+1)

The above cases are all possible. This means that the value of the function does not necessarily increase as x increases, since we do not know the function rule. Therefore, we cannot conclude with certainty that P(x+1)>P(x).