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Math Basketball Honors Pre-Calculus Mid-Chapter 3 Quiz Review

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How to play Math Basketball

- Your table group will be your team
- A problem will be displayed and your team will need to work together to find a solution to the problem in the time given.
- Only one member of the team may write during a given problem and that role must switch to a new team member before the next question.

How to play Math Basketball (cont.)

- Upon finding the solution, a team will raise their hands and I will confirm the solution
- But, be warned…a team may only raise their hand once to show me the solution…so make sure everyone on the team agrees on the solution before showing me…for showing me the wrong solution means scoring no points
- Every team (not just the first) may score 1 point if they raise their hand and show the correct answer

How to play Math Basketball cont.

- After the time allotted for a question has passed (and we see how the problem is solved), those teams that have scored 1 point on the question will have a chance to shoot for a 2nd point.
- So, each team has the possibility of scoring 2 points for each question
- The team that finishes last will get 1 point, second to last will get 2 points, and so on.

Anything that would fall into the category of cheating (or negative remarks towards another team) will result in negative points awarded to the team(s) involved.

Cheating

Question #1: Sketch and analyze the graph of the following function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.

Question #2: Sketch and analyze the graph of the following function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.

Question #3: The table shows the number of reported cases of chicken pox in the United States in 1980 and 2005.

If the number of reported cases of chicken pox is decreasing at an exponential rate, identify the rate of decline and write an exponential equation to model this situation.

Question #4: Use the model you found in #3 to predict when the number of cases will drop below 20,000.

Question #5

- Worldwide water usage in 1950 was about 294.2 million gallons. If water usage has grown at the described rate, estimate the amount of water used in 2000.
- 3% quarterly
- 3.05% continuously

Question #6

- Use the data in the table below and assume that the population of Miami-Dade County is growing exponentially. Identify the rate of growth and write an exponential equation to model this growth.

Question #7

- Use the model you found in #6 to predict in which year the population of Miami-Dade County will surpass 2.7 million.

Question #8

- The chance of having an automobile accident increases exponentially if the driver has consumed alcohol. The relationship is modeled below, where A is the percent chance of an accident and c is the driver’s blood alcohol concentration (BAC). The legal BAC is 0.08. What is the percent chance of having a car accident at this concentration?

Question #9

- Use the model from #8. What BAC would correspond to a 50% chance of having a car accident?

Question #10

- The Consumer Price Index (CPI) is an index number that measures the average price of consumer goods and services. A change in the CPI indicates the growth rate of inflation. In 1958, the CPI was 28.6, and in 2008, the CPI was 211.08.
- Determine the growth rate of inflation between 1958 and 2008. Use this rate to write an exponential equation to model this situation.
- What will be the CPI in 2015?

Question #12

- Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.

Question #13

- Sketch and analyze the graph of each function. Describe its domain, range, intercepts, asymptotes, end behavior, and where the function is increasing or decreasing.

Question #14

- Use the graph of f(x) = ln(x) to describe the transformation that results in each function. Then sketch the graphs of the functions.

a.

b.

Question #15

- The annual growth rate for an investment can be found using the formula below, where r is the annual growth rate, t is time in years, P is the present value, and P0 is the original investment. An investment of $10,000 was made in 2002 and had a value of $15,000 in 2009. What was the average annual growth rate of the investment?

Answers

1. D: (-∞, ∞) R: (0, ∞)

Intercept: y = 1 Asymptote: y = 0

End behavior: lim as x -∞ = ∞

lim as x ∞ = 0

Inc./Dec.: Decrease from (-∞, ∞)

2. D: (-∞, ∞) R: (0, ∞)

Intercept: y = 1 Asymptote: y = 0

End behavior: lim as x -∞ = 0

lim as x ∞ = ∞

Inc./Dec.: Increase from (-∞, ∞)

Answers (cont.)

8.

16.71%

10. 3.6496%, 220.66

11. a) 3.47 b) 4 c) -3 d) -2.197

12. D: (0, ∞) R: (-∞, ∞)

Intercept: x = 1 Asymptote: x = 0

End behavior: lim x -> 0+ = - ∞

lim x -> ∞ = ∞

Increase from (-∞, ∞)

Answers (cont.)

13. D: (0, ∞) R: (-∞, ∞)

Intercept: x = 1 Asymptote: x = 0

End behavior: lim x -> 0+ = ∞

lim x -> ∞ = - ∞

Decrease from (-∞, ∞)

14. It flips overs the x-axis and moves 3 to the left.

It shifts left 4 and up 3.

15. 5.79%.

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