Please Explain your reasoning
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.
Be sure to reference all sources using APA style.
1. When H = (constant)a^t and a>1, then H increases with time. If a<1, then H decreases with time. Which do you think is better?
2. pH is the -log(base10) of the H3O+ concentration in mole/liter
For further information and examples, see http://www.800mainstreet.com/acid_base/definitions-ph.html
Part 1: To determine whether a homebuilder would prefer the value of a in the exponential function H = p * a^t to be between 0 and 1 or larger than 1, we need to understand the behavior of exponential functions.
When the value of a is between 0 and 1, the exponential function H = p * a^t will exhibit decay. This means that as time (t) increases, the number of new homes built (H) will decrease gradually. In this case, the value of a represents the decay factor.
On the other hand, when the value of a is larger than 1, the exponential function H = p * a^t will exhibit growth. This means that as time (t) increases, the number of new homes built (H) will increase exponentially. In this case, the value of a represents the growth factor.
As a homebuilder looking for work, it would be preferable to have the value of a larger than 1 in the exponential function. This is because a larger value of a indicates a greater growth factor, which means that the number of new homes being built is increasing at a faster rate. This increases the chances of finding work as a homebuilder.
Part 2: The logarithmic formula that gives the pH of a substance is given by the equation:
pH = -log[H+]
In this equation:
- pH represents the measure of acidity or alkalinity of a substance.
- [H+] represents the concentration of hydrogen ions in moles per liter (mol/L).
To find the pH of a substance, you need to determine the concentration of hydrogen ions in that substance and then take the negative logarithm of that concentration.
To determine if a substance is acidic or basic, you need to look at the pH value. If the pH value is less than 7, the substance is acidic. If the pH value is greater than 7, the substance is basic. A pH value of 7 indicates a neutral substance.
To find the hydrogen ion content of a substance using the formula, you need to rearrange the equation:
[H+] = 10^(-pH)
In this equation:
- [H+] represents the concentration of hydrogen ions in moles per liter (mol/L).
- pH represents the pH value of the substance.
To calculate the hydrogen ion content, substitute the given pH value into the equation and evaluate it.
Remember to use appropriate units and round the answer to 10 decimal places or use scientific notation as required.
When referencing sources using APA style, include the author's name, publication year, title of the article or webpage, and the URL (if applicable). Also, cite any specific information or quotes used from these sources in the appropriate places within your response.