Math 115/Calc 1 Help Exponential Functions

In summary, an exponential function is a mathematical function in the form of f(x) = ab^x, where a and b are constants. It is characterized by a rapid increase or decrease in values as the input increases or decreases. To graph an exponential function, you can create a table of values or use a graphing calculator. The main difference between an exponential function and a polynomial function is the presence of a variable in the exponent. To solve exponential functions, you can use properties of logarithms or algebraic techniques. Some real-life applications of exponential functions include population growth, compound interest, and radioactive decay. They are also used in various fields to analyze natural and man-made processes.
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Homework Statement



Give a formula for the exponential function illustrated. The two points marked on the graph are A=(−1−17) and B=(1−2). The red horizontal line is given by y=−1, and is a horizontal asymptote of the function

The Graph:
http://tinyurl.com/3oywz8l
 
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FAQ: Math 115/Calc 1 Help Exponential Functions

What is an exponential function?

An exponential function is a mathematical function in the form of f(x) = ab^x, where a and b are constants. The variable x represents the exponent and b is the base of the function. Exponential functions are characterized by a rapid increase or decrease in values as the input increases or decreases.

How do I graph an exponential function?

To graph an exponential function, you can first create a table of values by choosing different values for x and calculating the corresponding values for f(x). Then, plot these points on a coordinate plane and connect them with a smooth curve. Alternatively, you can use a graphing calculator to graph the function directly.

What is the difference between an exponential function and a polynomial function?

The main difference between an exponential function and a polynomial function is the presence of a variable in the exponent in exponential functions. Polynomial functions, on the other hand, have a variable raised to a whole number power. Additionally, polynomial functions have a finite number of terms, while exponential functions have an infinite number of terms.

How do I solve exponential functions?

To solve exponential functions, you can use the properties of logarithms, which are the inverse of exponential functions. You can also use algebraic techniques such as factoring, completing the square, or the quadratic formula. Additionally, you can use a graphing calculator to find the intersection points of the exponential function and a linear function.

What are some real-life applications of exponential functions?

Exponential functions are commonly used to model population growth, compound interest, radioactive decay, and other phenomena that exhibit exponential growth or decay. They are also used in biology, economics, finance, and physics to analyze various natural and man-made processes.

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