7.1 Review Worksheet
7.1.1 Exponential Functions, Growth, and Decay Tell whether the function shows growth or decay. Then graph. 1. f ( x ) 2. f ( x ) = f x ( ) x = f x ( ) (1.3) x
1 3
1 3
3. f ( x ) = 10(2.7) x
4. The amount of freight transported by rail in the United States was about 580 billion ton-miles in 1960 and has been increasing at a rate of 2.32% per year since then. a. Write a function representing the amount of freight, in billions of ton-miles, transported annually (1960 = year 0).
b. Graph the function.
c. In what year would you predict that the number of ton-miles would have exceeded or would exceed 1 trillion (l000 billion)?
5. A quantity of insulin used to regulate sugar in the bloodstream breaks down by about 5% each minute. A body-weight adjusted dose is generally 10 units. a. Write a function representing the amount of the dose that remains after x minutes.
b. Use a calculator to graph the function.
c. About how much insulin remains after 10 minutes?
d. About how long does it take for half of the dose to remain?
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