standard_description: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
problem_activity: Task
Ari has collected data on how much her classmates study each week and how well they did on their recent math test. Here is part of the data, showing the percentage of each group (divided according to hours spent studying) who got different grades on the test:
| Weekly Hours $w$ Studying | C or below on test | B on test | A on test |
|---------------------------|--------------------|-----------|-----------|
|         $w \lt$ 3         |        50%         |    20%    |    30%    |
|     $3 \leq w \lt 6$      |        60%         |    25%    |    15%    |
|        $w \geq 6$         |        60%         |    20%    |    20%    |
What can you conclude about the percentage of Ari's classmates who got B's? What about the percent who got A's?
Looking at the table, Ari decides that in order to do well in her math class, she should not study more than 3 hours a week: she has a 30 percent chance of getting an A as long as she does not study more than 3 hours per week. Is Ari's reasoning valid?


aligns: no