Download Simplify the following expressions

Math 131
Linear Functions Review
Section 2.3
1. A new refrigerator sells for $799. Running it costs 8 cents per day.
(a) Express the cost (buying and running) of the refrigerator, C  x  , as a linear function of the number
of days, and give the domain of your function. (b) Find a complete graph for this problem situation, and
give the slope and y-intercept with appropriate units. (c) How much does it cost to keep your food cold
for the first year? (d) When will you have paid as much in daily costs as it cost you to buy the
refrigerator?
2. A car costs $7200 when new. Suppose its value, V (in dollars), depends linearly on its age, T (in
years), and decreases at a rate of $680 per year.
(a) Express the value of the car as a function of its age. (b) Identify the slope and y-intercept, including
their units. (c) Find a complete graph for the problem situation. (d) How much is the car worth when
it is 6.5 years old? (e) When is it worth half its original value? (f) When does the car have no resale
value? (g) Find the value of the car after 20 years. Comment on the meaning of your answer.
3. Suppose that a 25 pound bag of dog food costs $4.74, and a 10 pound bag costs $2.19. Assume that
there is a linear relationship between size of bag and the price of the bag.
(a) Find the formula for the price per bag as a function of the weight of the bag. (b) How much would a
30 pound bag cost? (c) Approximately what amount could be bought for $20?
4. The life expectancy of US citizens in 1950 was 65 and in 1970 it was 68.
(a) Find the linear function expressing the life expectancy of a US citizen as a function of time. For
simplicity, let t be the number of years after 1950. (b) Find the life expectancy in the year 2010. (c)
When will the life expectancy reach 105?
5. The amount of heat, H (in joules), required to convert one gram of water into vapor is linearly related
to the temperature T (in C ) of the atmosphere. At 10C this conversion requires 2480 joules, and
each increase in temperature of 15C lowers the amount of heat needed by 40 joules.
(a) Write H as a linear function of T. (b) How much heat is required to vaporize one gram of water at
20C ? (c) 2000 joules would vaporize one gram of water at what temperature?
Some Answers: 1(a) C  x   799  0.08x ; (c) C  365  828.2 ; (d) 27.4 years. 2(a)
V  7200  680t ; (d) $2780; (e) 5.3 years; (f) 10.6 years. 3(a) p  0.17 w  0.49 ; (b) $5.59;
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7520
(c) 115 lbs. 4(a) y  0.15t  65 ; (b) 74 years; (c) 2216. 5(a) H T   T 
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(b) 2453.3 j; (c) 190C .