EOCT Word Problems



1. The Houston Astrodome was the first baseball and football stadium to be completely enclosed. It was completed in 1965 at a cost of 45.35 million dollars. Construction costs have increased by approximately 6% each year since 1965. How much would it cost to build the Astrodome today?

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2. A new car was purchased in 1990 for $14,000. The value of the car, V, decreased by 26%. What is the value of the car in 1993?

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3. $1200 is deposited in an account that pays 6% annual interest, compounded quarterly. Find the balance after five years.

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4. How much must you deposit in an account that pays 6.5% interest, compounded semi-annually, to have a balance of $5000 in 15 years.

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5. In 1984, the population of Greensboro, NC was 197,910. According to the US Census Bureau, Greensboro has been growing at the rate 6.9% annually since 1984. What equation models the population of Greensboro t years after 1984?

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6. The equation c = 523, 430(1.193)t models United States copper production in pounds from 1987 – 1992. Which statement best interprets the coefficient and base of this equation?

A) The copper production in 1987 was 523, 430 pounds, and it had been increasing at a rate of 1.93% per year during that period.

B) The copper production in 1987 was 523,430 pounds, and it had been increasing at a rate of 19.3% per year during that period.

C) The copper production increased by a factor of 523,430x1.193 pounds per year during that period.

D) The copper production at the beginning of 1987 was at 1.193 pounds, and it had been increasing by a factor of 523,430 pounds per year during that period.

7. Mr. Jones bought a piece of property for $25,000. If the property appreciates at a rate of 10% per year, what will be its approximate value in 7 ½ years?

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8. An $18,000 car depreciates at a rate of 16% per year. How old will the car be when it is worth $12,000?

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9. What function models the population of Ethiopia from 1940 to 2000 (let x = 0 in 1940)?

|Year |Population of Ethiopia |

| |(in millions) |

|1940 |16 |

|1950 |20 |

|1960 |25 |

|1970 |31 |

|1980 |39 |

|1990 |50 |

|2000 |64 |

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10. A medicine contains 400 units of an antibiotic per milliliter. The medicine decomposes over time. The decomposition process is summarized in the table.

|Days(d) |3 |6 |7 |9 |11 |13 |18 |

|Units of Antibiotic |380.1 |361.2 |355.1 |343.3 |331.8 |320.7 |294.6 |

|(a) (per milliliter| | | | | | | |

What equation is the best model for this data? __________________________________

11. The Wongs bought a new house three years ago for $92,000. The house is now worth $113,000. Assuming a steady annual growth rate, approximately what was the yearly rate of appreciation?

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12. How long would it take an investment to double if it is invested at 4% compounded monthly?

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13. The hourly rate of your new job is $5.00 per hour. You expect a raise of 9% each year. At the end of your first year, you receive your first raise. What will your hourly rate be at the end of your fifth year?

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14. In an over-fished area, the catch of a certain fish is decreasing at an average rate 8% per year. If this decline persists, how long will it take for the catch to reach half of the amount before the decline?

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15. Alex invests $2000 in an account that has 6% annual rate of growth. To the nearest year, when will the investment be worth $3600?

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16. How many days will it take a culture of bacteria to increase from 2000 to 50,000 if the growth rate per day is 93.2% ?

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17. In a laboratory, an organism grows from 100 to 250 in 8 hours. What is the hourly growth rate in the growth formula y = a(1+r)t?

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18. A furniture store is closing out its business. Each week the owner lowers prices by 25%. After how many weeks will the sale price of a $500 item drop below $100?

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19. Ten years ago, Mr. and Mrs. Boyce bought a house for $96,000. Their home is now worth $125,000. Assuming a steady rate of growth, what was the annual rate of appreciation?

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20. Ten years ago, Tiffany’s mother bought a new car for $9000. Tiffany is now going to buy the car for $900. Assuming a steady rate of depreciation, what was the approximate annual rate of depreciation?

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21. The Greens bought a condominium for $83,000. Assuming that its value will appreciate 6% per year, how much will the condo be worth in five years when the Greens are ready to move?

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Use the following information for questions 22 and 23:

The Fresh and Green Company has a savings plan for its employees. If the employee makes an initial contribution of $1000, the company pays 8% interest compounded quarterly.

24. If an employee participating in the plan withdraws the balance of the account after five years, how much will the company have paid into the account?

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25. If an employee participating in the plan withdraws the balance of the account after thirty-five years, how much will the company have paid into the account?

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26. The first permanent English colony in America was established in Jamestown, Virginia in 1607. From 1620 through 1780, the population P of colonial America can be modeled by the equation

P = 8863(1.04)t where t is the number of years since 1620. When was the population of colonial America about 345,000?

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