# Applications of Exponential and Logarithmic Functions

Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents.

Find the hydrogen ion content of a substance of your choice. Using this hydrogen ion content, show how to find the pH of the substance using the formula. Is this substance acidic or basic? Why?

Round the pH to three decimal places.

Part 2: Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * at where p is the number of cars on the road on the first day recorded. If you commuted to work each day along 1st Avenue, would you prefer that the value of be between 0 and 1 or larger than 1? Explain your reasoning. Be sure to reference your sources using APA style.

Typing hint: Type formula above as C = p * a^t

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#### Solution Preview

Please see the attached file.

From the website

http://www.elmhurst.edu/~chm/vchembook/184ph.html

we have the formula for pH:

pH = - log [H+]

The variable in this equation is [H+], which is the concentration of hydrogen ion in solution.

Say we have in a 0.01 mol/L solution of HCl it is approximated that there is a concentration of 0.01 mol/L dissolved hydrogen ions. So its pH is:

pH = - log(0.01) ...

#### Solution Summary

Applications of Exponential and Logarithmic Functions are investigated.