Arithmetic and Geometric Sequences: Word Problems Name

Arithmetic and Geometric Sequences: Word Problems

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1. You throw a SuperBall on the cement as hard as you can and watch it bounce until it stops. You notice the first bounce reaches a height of 200ft, but the second bounce reaches 50% of that height. What type of sequence is represented by the height of the ball? Write an explicit equation to model the situation. How high will the 7th bounce reach (round to the nearest tenth of a foot)?

2. According to the U.S. Census Bureau, the population of the United States in 2008 was 304 million people. In addition, the population of the United States was growing at a rate of 1.1% per year.

A) Write the recursive and explicit formulas that would model this situation.

B) Use your equation to predict the United States population in 2050. Round your answer to the nearest million.

3. Players on the Math Wiz Game Show are playing for either Prize A or Prize B. After the game, the winners will have 10 seconds to decide which prize to choose. They get to keep the money from the twentieth day.

Prize A: Start with $100, earn $100 each day, for 20 days. Keep only the money from the twentieth day.

Prize B: Start with $.01, double your money each day, for 20 days. Keep only the money from the twentieth day.

Investigate how much money each prize is worth by making a table or writing a sequence. Write a recursive and explicit formula for each prize. Determine which would be better on the twentieth day. Then decide which prize you would take.

4. If you had $145 in your account at the beginning of the year. And your account grew by 5% each month. How much money would be in your account after 10 months (round to the nearest cent)? Write an explicit and recursive formula to help model this situation.

5. A population of deer in a certain area is decreasing by 15% each year. The population had 2040 deer in it in the year 2000 (year 0). How many deer are there in the population in year 2020 (round to the nearest whole number)? Write the explicit and recursive formulas that would model this situation.

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