Let's start with the following situation:

The pH level in a person's mouth changes after eating food containing sugar.
The formula L = −  20.4m m² + 36 + 6.5 can be used to find L, the acid level, for m, the number of minutes since the food was eaten. A graph of the function is shown below.

1. Estimate the acid level for after 15 minutes.
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Check Your Answer

Answer: About 5.3

L = − twenty point four times fifteen over fifteen squared plus thirty-six 20.4(15) (15)² + 36 + 6.5 = − three hundred six over two hundred and sixty one 306 261 + 6.5 = -1.2 + 6.5 = 5.3

2. Estimate the time(s) when the acid level would be 6.0
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Check Your Answer
Answer: About 1 minute and about 40 minutes
6.0 = − twenty point four m over m squared plus thirty-six 20.4m m² + 36 + 6.5
−0.5 = − twenty point four m over m squared plus thirty-six 20.4m m² + 36
−0.5m² − 18 = −20.4m
0 = .5m² − 20.4m + 18
m = numerator twenty point four plus or minus the square root of twenty point four squared minus 4 times point five times eighteen over two times point five 20.4 ± √(20.4)² − 4(.5)(18) 2(.5)
m = twenty point four plus or minus the square root of three hundred eighty point sixteen over one 20.4 ± √380.16 1
m = .9 or m = 39.9

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