Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right. pH is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. The variable x represents the amount of hydronium ions, and f(x) gives the pH level. Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3. Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.