To see just how quickly f(x) = 2" increases, let's perform the following thought experiment. Suppose we start with a piece of paper that is a a° = 1 for a + 0. You can see from Figure 2 that there are two kinds of exponential functions: If 0 1, the func- tion increases rapidly (see the margin note). thousandth of an inch thick, and we fold it in half 50 times. Each time we y = 9 y = ()" y = ( y = ( y = 10* y= 5* y = 3* y = 2" fold the paper, the thickness of the paper stack doubles, so the thickness of the resulting stack would be 250/1000 inches. How thick do you y A think that is? It works out to be more than 17 million miles! FIGURE 2 A family of exponential functions
To see just how quickly f(x) = 2" increases, let's perform the following thought experiment. Suppose we start with a piece of paper that is a a° = 1 for a + 0. You can see from Figure 2 that there are two kinds of exponential functions: If 0 1, the func- tion increases rapidly (see the margin note). thousandth of an inch thick, and we fold it in half 50 times. Each time we y = 9 y = ()" y = ( y = ( y = 10* y= 5* y = 3* y = 2" fold the paper, the thickness of the paper stack doubles, so the thickness of the resulting stack would be 250/1000 inches. How thick do you y A think that is? It works out to be more than 17 million miles! FIGURE 2 A family of exponential functions
Graph the function, not by plotting points, but by starting from the graphs in the figure. State the domain, range and asymptote.
g(x) = 1 - 3-x
Transcribed Image Text:To see just how quickly f(x) = 2"
increases, let's perform the following
thought experiment. Suppose we
start with a piece of paper that is a
a° = 1 for a + 0. You can see from Figure 2 that there are two kinds of exponential
functions: If 0 <a<1, the exponential function decreases rapidly. If a > 1, the func-
tion increases rapidly (see the margin note).
thousandth of an inch thick, and we
fold it in half 50 times. Each time we
y = 9 y = ()"
y = ( y =
( y = 10*
y= 5*
y = 3*
y = 2"
fold the paper, the thickness of the
paper stack doubles, so the thickness
of the resulting stack would be
250/1000 inches. How thick do you
y A
think that is? It works out to be more
than 17 million miles!
FIGURE 2 A family of exponential
functions
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