Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: he second base is an irrational number, e ≈ 2.718, called the natural base. We will more formally discuss the origins of this number in Section 6.5. For now, it is enough to know that since e > 1, f (x) = ex is an increasing exponential function. The following examples offer a glimpse as to the kind of real-world phenomena these functions can model. Example 6.1.1. The value of a car can be modeled by V (x) = 25 car in years and V (x) is the value in thousands of dollars. 4x 5, where x ≥ 0 is age of the 1. Find and interpret V (0). 2. Sketch the graph of y = V (x) using transformations. 3. Find and interpret the horizontal asymptote of the graph you found in 2. Solution. 0 4 1. To find V (0), we replace x with 0 to obtain V (0) = 25 5 = 25. Since x represents the age of the car in years, x = 0 corresponds to the car being brand new. Since V (x) is measured in thousands of dollars, V (0) = 25 corresponds to a value of $25, 000. Putting it all together, we interpret V (0) = 25 to mean the purchase price of the car was $25, 000. x x 4 2. To graph y = 25 5 , we start with the basic exponential function f (x)...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online