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
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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Graph the function, not by plotting points, but by starting from the graphs in the figure. State the domain, range and asymptote.
f(x) = -3x
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