Question

The percentage of teenagers who will have more than one episode of depression within two years is between 15% and39%, inclusive. Let p be the percentage of teenagers who will have more than one episode of depression within twoyears. Describe the values of p using inequality notation, interval notation, and a graph.

Answer 1

• Inequality notation: 15 ≤ p ≤ 39

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• Interval notation: [15, 39]

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• Graph: ,see explanation section

Step-by-step explanation

If p is the percentage of teenagers who will have more than one episode of depression within two years, and this is between 15% and 39%, inclusive, it means that p is greater than or equal to 15 and less than or equal to 39. In inequality notation, 15 ≤ p ≤ 39.

Interval notation is the one where we use parenthesis () and/or brackets [] to express an interval. In this case, the interval is continuous between 15 and 39 and includes the two values, so we have to use brackets: [15, 39].

In a graph, we can draw a number line and highlight the line between 15 and 39, using filled circles to include those two values - sometimes brackets are used instead,