Extra Credit Practice Sheet – Due Tomorrow
Name: ___________________________________________________________________
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Work must be shown to receive full credit.
1. Consider the following function
a. What is the specific name of this exponential function?
b. What is the domain and range?
c. Name two points on the graph.
d. Identify any asymptotes.
2. In 1991, the population of Tokyo was 27.245 million. The average growth rate is 2.86% annually.
a. Write an equation to describe the situation, and find what the population should be in 2012.
b. Find what the population of Tokyo was in 1981.
3. Radioactive Strontium-90 has a half-life of 29 years. Suppose a substance starts with 100 grams.
a. Write an equation to describe the situation, and find the amount of Strontium-90 left after 174 years.
b. How much Stontium-90 will be left after 4.5 half lives?
4. The pesticide DDT was widely used in the United States until its ban in 1972. DDT is toxic to a wide
range of animals and aquatic life, and is suspected to cause cancer in humans. The half-life of DDT is
approximately 15 years. If large crop of corn initially used 15,000 grams of DDT in 1970.
a. Write an equation to describe the situation, and find the number of grams remaining in 2012.
5. The population of a middle-eastern city increases by 30% every 6 years. Its population in 1990 was
152,000.
a. Write an equation to describe the situation, and find what the population was in 2008.
b. Find what the population was in 1978.
6. Carbon has a half-life of 5730 years.
a. How many years are in 4 half-life periods?
b. If we originally have 20 g of carbon, how much will remain after 2000 years?
7. Each year sponsors put on a tennis tournament. Play starts with 8,194 participants. During each round,
half of the players are eliminated.
a. Write an equation describing the situation, and find how many players remain after 10 rounds.
8. Upon looking at a graph, there is a y-intercept of
. The graph looks to be decreasing 10% for each x
value. Derive an equation that would describe the given graph.
9. There is a well-known fable about a man from India who invented the game of chess, as a gift for his king. The
king was so pleased with the game that he offered to grant the man any request within reason. The man asked for
one grain of wheat to be placed on the first square of the chess board, two grains to be placed on the second square,
four on the third, eight on the fourth, etc., doubling the number of grains of wheat each time, until all 64 squares on
the board had been used. The king, thinking this to be a small request, agreed. A chess board has 64 squares. How
many grains of wheat did the king have to place on the 64th square of the chess board?