3. What Is the Common Ratio in the Following Sequence?
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Unit 16 Review Worksheet
1. A shoe store is discounting shoes each month. A pair of shoes cost $80. The table shows the discount prices for several months. Find the cost of shoes after 8 months. Round your answer to the nearest cent.
Month Price 1 $80.00 2 $72.00 3 $64.80
2. The first term in a geometric sequence is -0.25 and the common ratio is -3. Find the 10th term.
3. What is the common ratio in the following sequence?
40, 10, 5/2, 5/8, …
4. The twelfth term in a geometric sequence is -708,588 and the common ratio is 3. What is the first term?
5. The population of a town is 2,500 and is decreasing at a rate of 3% per year. What will be the population after 5 years?
6. Twelve students at Klein Collins passed an AP test in 2000. The number of students who passed the test increased by 16.4% each year thereafter. Find the number of students that will pass it this year.
7. Does the function represent growth or decay? Explain why. y = 3 (0.83)x
8. What is the percent of growth or decay? 9. The population of a small Midwestern town is 4500. The population is decreasing at a rate of 1.5% per year x years after the year 2000. Write an exponential function to model this situation. Then find the year when the population falls below 3000.
10. A condo in Austin, Texas was worth $80,000 in 1990. The value of the condo increased by an average of 3% each year. Write an exponential function to model this situation and use it to predict its value this year.
11. During the recent drought, the fish population at Lake Limestone was decreasing at a rate of 2% per month. At the beginning of that year, the fish population was about 12,450. If the trend continued, what would the population of the lake be after August (when I went for Labor Day)?
12. The half-life of Tritium is 12 years. How much is left from a 500 mg sample after 6 decades?
13. Evaluate y = 3 · 2x for the domain {6, 7, 8}.
14. The time it takes to drive between two cities varies inversely as speed. Dolores can drive between Houston, Texas and San Antonio, Texas in 3.5 hours at 60 mph. How long will the trip take if she drives 70 mph (to the nearest tenth).
15. Tell whether the relationship is an inverse variation:
y x 2 12 3 8 4 6 x y 0 500 1 750 2 1125
16. Write a function for the following relationship:
17. Graph y = 3 · 1.5x