Group+5+-+Graphing+Exponentials+and+Logs

=**Group 5**= =Group Members:Eden, Annie, Suzanna=

- //Exponential functions// is an equation in the form y = a^x, where a>0 and a does not equal zero. - If a<1, then f is a decreasing function and if a>, then f is an increasing function - The domain is set of real numbers - The range is the set of strictly positive real numbers - The function is continuous in its domain - The x-axis is horizontal asymptote - The inverse function of an exponential function is called a logarithmic function - Given the exponential function f(x) = a^x o the graph of g(x) = a^-x will be a reflection of f(x) across the y axis o the graph of h(x) = ka^x will be a vertical stretch of f(x) but will have the same general shape. o The graph m(x) = -ka^x will be a reflection of g(x) = a^x across the x-axis o ….more of these type of graphs can be seen on our gsp sketch of f(x) = a^x - exponential properties o ( a^r)( a^s) = a^(r+s) o a^r / a^s = f(x) = a^(r-s ) o ( (a^r))^s = a^(rs) o ( a^r)(b^x) = (ab)^r - //natural exponential// function is a function f(x) = //e^//x where //e// = 2.71828182846… which is an irrational number. - //e// = (1 + 1/n)n where n approaches infinity - exponential function is used to show when a constant change in the independent variable gives the same proportional change (increase or decrease) in the department variable… “grows” or “decays” at a rate proportional to its current value - The number //e// occurs naturally in any situation where a quantity increases at a rate proportional to its value, such as a bank account producing interest, or a population increasing as its members reproduce. || Eden is sick. Suzie and Annie worked on adding instructions to the interactive tool. We also added a page to dynamically demonstrate the inverse of an exponential function. || Suzie and Annie chose problems of varying difficulty to work on over the weekend. ||
 * Date || Humor || Conceptual Video || Interactive || Extra Worked Problems ||
 * Nov 18 ||  || Eden wrkng on properties of e || Annie working on grphing ||   ||
 * Nov 23 ||  ||  ** Eden posted properties of exponential functions to be mentioned on our conceptual video **** Exponential functions **
 * Nov 30 || Suzi will be working on the humor part of the video. || Eden is working on the script for the conceptual video on the properties of exponentials and a practical problem. Annie and Suzi are working on the other part of the conceptual about the inverse of the exponential function. || Annie is going to add instructions to the interactive tool. || Annie and Suzi are working on extra worked problems. ||

Graphing Exponentials media type="youtube" key="zlGuQm91mgE?fs=1" height="385" width="480"

Graphing Logs media type="youtube" key="ey8rT90OIkg?fs=1" height="385" width="480"