Math Patterns and Functions 11.1

1. In 1990 there were 249,464,000 people in the United States. In 1999, there were 272,690,000 people. What was the average yearly population increase between these years?

2. The population of Cityville is currently 7,680. In 6 years, the population is projected to be 11,570 residents. What is the projected change in residents per year over this time period? Round your answer to the nearest person.

3. A babysitter charges $7.50 an hour and rounds up to $7.50 for each fraction of an hour. Which graph of a function below models the situation?

4. The half life of radioactive material means that the radioactivity of that material is halved every x years. If x = 1,250 years, what percent of the original radioactivity does the material have after 6,250 years?

5. Julie has $1,000.00 to invest for 3 years at a rate of 5% interest compounded annually. She uses the following formula to determine the value of her investment after 3 years: M = P (1 + r) n. M = the final amount including interest P = principle r = rate of interest n = number of years. How much money will Julie have including interest after 3 years?

6. Population growth can be modeled by exponential growth functions P =Po ax, where Po is the initial population, a is the annual growth factor (equal to one plus the annual growth rate), and x is the number of years after the initial population year. In the United States in 1900, the population was 76 million with the annual increase of 7%. If the growth continued at this annual rate, what equation models the population in 1910?

7. The population of rabbits at a zoo starts at 3 and grows to 243 after 4 years. Part A By what factor is the population growing per year? Part B What was the population after 3 years? What will it be after 5?

8. What happens to the graph of the equation, y = x2 + 4x + c, when you increase the value of c?

9. In which direction will the graph of y = -2x2 + 5x + 4 open?

10. The chances of flipping a penny and getting n heads out of n attempts is 1/2(n). What is the chance of getting 6 heads out of 6 attempts?

12. Jose throws a ball upward at a rate of 10 meters per second from an initial height of 1 meter. The height of the ball above the ground can be approximated by h = -5t 2 + 10t + 1 where t represents the amount of time, in seconds, since the ball has been released. What is the maximum height that the ball reaches? The x coordinate for the vertex is found with the following formula: -b/2a

13. An object that is projected straight downward with initial velocity v feet per second travels a distance s = vt +16t2, where t =time in seconds. If Ramon is standing on a balcony 84 feet above the ground and throws a penny straight down with an initial velocity of 10 feet per second, in how many seconds will it reach the ground?

14. Which of the following does not represent a function?

15. Which of the following tables of values fit’s the equation, y = x2 + x – 3?

16. Neil scored 70 out of 100 points on his first test. Each test he took after that he got half as many wrong as he did on the test before. What was Neil’s score on his third test, rounded to the nearest point?

17. The rise between the first and second floor of a building is 12 ft. The horizontal run is 108 inches. What is the slope of the stairway?

18. Jorge earns a salary of $500 each week and earns a commission of 5% of any merchandise he sells. What equation in slope-intercept form describes Jorge’s potential income each month? (I = income and s = amount of sales)