# Logarithmic and exponential 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 pH of a substance of your choice that is alkaline (basic). Using this pH, show how to find the hydrogen ion concentration, [H+], of the substance using the formula. Discuss the meaning of pH and [H+], the pH scale and why your chosen substance is alkaline. Use scientific notation or enough decimal places so that your answer has at least 3 place values. For example, either use 3.44*10-9 or 0.00000000344.

Part 2: 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. Be sure to reference your sources using APA style.

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#### Solution Summary

This provides examples of working with real-life logarithmic and exponential functions.