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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
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.
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)...
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