# Applications of Logarithmic and Exponential Equations

Part 1: Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , where p is the number of new homes built in the first year recorded. If you were a homebuilder looking for work, would you prefer that the value of a to be between 0 and 1 or larger than 1? Explain your reasoning.

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

Part 2: 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 pH factor of a substance of your choice. Is this substance acidic or basic? Why?

Using this pH, show how to find the hydrogen ion content of the substance using the formula. Round to 10 decimal places or write your answer using scientific notation. Include units on your answer.

Typing hint: 2.3 * 10^4 is an example of a number typed in scientific notation. Note that it is inappropriate to use decimals in the exponents of numbers written in scientific notation.

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#### Solution Summary

Logarithmic and Exponential Equations are investigated. The solution is detailed and well presented.