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Directions: Grab your paper, pencil, and graph paper. Read carefully!
1. |
A classic Mustang car is purchased for $28,000 and is expected to increase in value each year by $1400.
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a) Write the equation of a function to represent the increase in the value of the car in relation to the number of years after purchase.
Identify your variables.
b) At what rate is the price of the car increasing?
c) What will be the value of the car 10 years after its purchase?
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2. |
Water is leaking from a full 5-gallon pail at a constant rate as shown.
a) At what rate is the water leaking?
b) Write an equation for a function representing the relationship between the number of gallons of water in the pail, and the number of hours that have passed.
c) How many gallons of water remain in the pail after 4 hours?
d) How many gallons of water have drained out of the pail after 6 hours?
e) How long does it take to empty the pail? |
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3. |
Different horses have the capacity to run at different speeds. If it were possible for horses to maintain top running speed for extended periods of time (which they cannot do), the data may look like that shown in this question.
a) State the ordered pairs associated with a time of 20 minutes for both horses.
b) Write an equation for the function representing the average horse.
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Race Horse
y = 0.73x,
where y = distance in miles
and x = time in minutes.
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c) In a time of 60 minutes, how much farther, in miles, did the race horse travel than the average horse?
d) What does slope represent in this problem?
State the slope associated with the equation for each horse.
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4. |
Colleen has $740 in her savings account, and she is starting a new job. She wants to deposit $25 from her new paycheck each week into her savings account.
a) Complete the table at the right.
b) Write a function to model the money in her savings account as a function of the number of weeks she has been saving. Identify your variables.
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Number
of Weeks |
Total in Savings |
| 0 |
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| 1 |
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| 2 |
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| 3 |
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| 12 |
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| 52 |
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You may assume that the $25 is the only amount being added to the account,
and that no withdrawals occur. |
| c) If Colleen continues these deposits for two years, what limitations should be placed on the domain of your function?
d) What amount of savings will she have at the end of two years?
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5. |
A book store has decided to sell Jason's Graphic Novel. The novel will sell for $15.50 a copy.
a) What would be the most convenient interval to be placed on the vertical axis?
b) Write the equation for a function representing input as the number of novels sold, and output the amount of dollars paid.
Have a key for variables.
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c) Graph the function.
d) What, if any, restrictions need to be placed on this function? Explain. |
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6. |
Adding sugar to water raises the boiling point of the water. Adding 1 gram of sugar increases the boiling point of 1 liter of water by 0.94ºF. This effect is linear.
a) Write the equation of a function to represent this situation.
b) Graph the function using axes as shown at the right.
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c) State any needed restrictions for the function based upon the graph.
d) State the slope of this function? What does the slope represent?
e) Water boils at 212ºF. What is the boiling point of 1 liter of water if 6 grams of sugar are added?
f) If the domain is increased beyond 10 grams, what would be the boiling point in degrees when adding 24 grams of sugar?
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7. |
A new skateboarding park charges a $4 entry fee and an hourly charge as shown in the table at the right.
a) Explain how you can determine, from looking at the table, that this data is linear.
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b) Write the equation of a function representing the relationship between the cost, c, and the number of hours, h, spent skateboarding.
c) What is the hourly fee being charged?
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8. |
A car is being lowered onto a barge to be shipped abroad. When the car is in position to be vertically lowered, it is 50 feet above the barge. After 14 seconds of lowering, the car is 29 feet above the barge. After 30 seconds, the car is 5 feet above the barge. The car is being lowered at a constant rate.
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a) Express the two statements of information regarding the lowering of the car as ordered pairs.
Use s = seconds as input, and h = feet above the barge as output.
b) How do we know that this problem is a "linear" relationship?
c) Using the information from part a, calculate and label the rate of change, Δh/Δs. Explain what this rate of change is telling you.
d) How long will it take for the car to land on the barge?
e) Write an equation for the function representing the height, h, of the car above the barge after s seconds of lowering time. |
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