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Plains, Lines and Automobiles
1. Mr. Slater paid $32,000 for a car. Suppose that the car depreciates linearly at the rate
of 15% per year.
a. Write an equation for the value, V, of the car after t years.
V(t) = _______________________________
b. Graph the equation – be very careful to use appropriate windows.
Windows:
Xmin: _________
Xmax: _________
Ymin: __________
Ymax: __________
c. Use the graph to determine how long it will take for the value of the car to
depreciate to $3000.
____________________
d. Use the graph to estimate how long it will take for the car to lose all of its
value.
____________________
2. A communications satellite transmits 1.8 million messages per year. Assume the
number of messages will increase at a constant rate of 10% per year.
a.
Write an equation of the number of messages, N, that will be transmitted after t
years.
____________________________________
b. Graph the equation.
Windows:
Xmin: _________
Xmax: _________
Ymin: __________
Ymax: __________
c. Use the graph to estimate how man messages will be transmitted 2 years from
now. Round your answer to the nearest million.
____________________
d. Use the graph to estimate how many messages will be transmitted 5 years from
now.
____________________
3. A coffee company sells boxes of K-cups containing decaf and caffeinated K-cups.
Caffeinated sells for $.50 per K-cup and decaf sell for $.35 per cup. If a box containing 2
dozen K-cups sells for $11.20, how many of each kind is in the box?
Price per
Quantity
Equation 1: ________________________________
Equation 2: ________________________________
Answer: _______________
Total Cost
4. You plan to spend $127,000 on 20 commercials. A commercial spot during Two and
a Half Men costs $5000. The same commercial during a locally televised elementary
school swim meet is $8000. How many commercials of each kind can be purchased?
Price per
Quantity
Total Cost
Equation 1: ________________________________
Equation 2: ________________________________
Answer: _______________
5. A math whiz can do a hard problem in 3 hours and an easier one in 2 hours. She
charges $40 to do a hard problem and $30 to do an easy one. The mathematician wishes
to work 40 hours per week and to earn $560 per week. How many of each kind of must
she turn each week?
Price per
Quantity
Total Cost
Equation 1: ________________________________
Equation 2: ________________________________
Answer: _______________
6. An apartment building contains 80 units. Some of these are one-bedroom units
renting for $425 per month and some are two-bedroom units renting for $550 per month.
When the building is entirely rented, the total monthly rental income is $38,375. How
many apartments of each type are there?
Price per
Quantity
Total Cost
Equation 1: ________________________________
Equation 2: ________________________________
Answer: _______________
7. An 18% alcohol solution is mixed with a 45% alcohol solution to produce 12 ounces
of 36% alcohol solution. How many ounces of the two kinds of solution are necessary?
Price per
Quantity
Equation 1: ________________________________
Equation 2: ________________________________
Answer: _______________
Total Cost