# C11

Drew & DubĂ¨

Question: Describe and translate between graphical, tabular, written and symbolic representations of exponential and logarithmic relationships

Answer: Exponential and Logarithmic relationships can be shown in four different ways. These are symbolic, graphical, written, and tabular

• Symbolic- Symbolic is the fancy word for equation form. General exponential form looks like y=a(b)(x/c)+d. A stands for the starting point, and is also the y-intercept. B stands for the common ratio. C stands for the it takes to change by the common ratio. Finally D stands for the change in the Horizontal Asymptote. The general logarithmic form looks like this y=logb(x). If the base which is repersented by B is not stated it is asumed that it is 10.

Ex/ y=4(2)(x/3)+1 and y=log2.5(x)

• Graphical- Graphical is the method of showing it in graph form. A graph can be derived from both of the Symbolic versions of the exponential and logarithmic equations.

Ex/    > y=4(2)(x/3)+1                                                                                             > y=log2.5(x)

• Written-  Written is pretty much the equation explained in a sentence.

Ex/ Exponential: An exponential growth function with a y-intercept of 3 that doubles in y values every third x value.

Logarithmic: The inverse of the exponential function of x=2.5y

• Tabular- Tabular is the method of showing the exponential and logarithmic functions in a table.
Ex/

•  Sample Problem-  Symbolic to Written: y=5(2)(x/7)+3 is an exponential growth function with a y-intercept of 5 that doubles in y values every seventh x value and the horizontal asymptote is raised up three on the x axis. y=log7(x) is the inverse of the exponential function of x=7y