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).
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.
P(x+1)=P(x). Here, the number of people with cell phones x+1 years and x years after 1990 are the same.
P(x+1)< P(x). Here, the number of people with cell phones x+1 years after 1990 is less than the number of people with cell phones x years after 1990.
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).
