Helen Keller Middle School's New Haven Math Trail
 | This question can be completed
at any time, but is particularly appropriate after lunch!
During your lunch, you might have something sweet to eat or have a soda. When you eat something sweet, the enzymes in your saliva begin to work and lower the natural pH level in your mouth (pH is a chemical measurement). We can model this phenomenon with the equation: pH = 6.5 - ---------------------------- t^2 + 36 where t is the time in minutes after you have finished eating something sweet. Demineralization of tooth enamel (cavities) begins to occur when pH falls below 5.5 and stays there for an extended period. Enter the equation in Y= on your graphing calculator. In this case "pH" is "y" and "t" is "x". Be sure to enter this formula carefully. It will require two sets of parentheses. Set the window on your calculator as follows: XMIN = 0 XMAX = 30 YMIN = 4 YMAX = 7 Answer the following questions: a. What is the "natural" pH in your mouth, before you've eaten anything? b. After how many minutes does the pH go below 5.5? c. What is the lowest that the pH gets? d. When is the pH back to normal again (above 5.5)? |
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