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verify this analytically by thinking about what happens as we take larger and larger powers
of 5 .) This means as the car gets older, its value diminishes to 0. 6.1 Introduction to Exponential and Logarithmic Functions 333 The function in the previous example is often called a ‘decay curve’. Increasing exponential functions are used to model ‘growth curves’ and we shall see several diﬀerent examples of those in
Section 6.5. For now, we present another common decay curve which will serve as the basis for
further study of exponential functions. Although it may look more complicated than the previous example, it is actually just a basic exponential function which has been modiﬁed by a few
transformations from Section 1.8.
Example 6.1.2. According to Newton’s Law of Cooling7 the temperature of coﬀee T (in degrees
Fahrenheit) t minutes after it is served can be modeled by T (t) = 70 + 90e−0.1t .
1. Find and interpret T (0).
2. Sketch the graph of y = T (t) using transformations.
3. Find and interpret th...
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