Mathematics 1090
PRACTICE EXAM I
Spring 2004
1. Find the slope-intercept equation for the following lines:
(a) The line of equation 2y + 3x + 2 = 0
(b) The line passing through the points (1, 2) and (−1, 3)
(c) The line of slope 2 passing through the point (1, 1)
(d) The line parallel to y = 2x + 3 and passing through (0, 1)
(e) The line perpendicular to y = x + 2 and passing through (1, 0)
2. Suppose that the cost of a business property is $720000. The owning company wants
to use a straight-line depreciation schedule for a period of 120 months. If y is the
value of the property after x months, write the linear equation of the depreciation
schedule.
3. The total amount of a simple investment rate is given by
A(t) = P + P rt
where P is the principal investment, r is the yearly rate and t is the time (in years,
i.e. t = 0 when you invest the money and for instance the amount of money after 10
years is A(10), i.e. when t = 10).
You want to invest $10000, and your goal is to have $14000 after 8 years. For what
rate r can you achieve this goal?
4. You want to invest money so that if you decide to cash it out after 4 years you would
have $8000 and if you finally decide to cash it out after 10 years you would have
$15000. Find the equation of the line representing the amount of money A in function of the elapsed time t (since the investment) that would match your expectations.
Then compare with the formula of the preceding exercise to determine the rate and
the principal investment to achieve your goals.
5. You want to repaint your house. You calculated that you need 15 gallons of paint. At
the paint store they only sell a thick paint that you must dilute with a special solvent.
The salesman tells you that you must prepare a solution containing 10% of solvent
to have a good result. How many gallons of pure paint and solvent must you buy to
prepare the 15 gallons of diluted paint?
6. Find
( the market equilibrium for the following laws of supply and demand.
p = − 51 q + 200
, calculate also the M.E. in the case of a tax. of $6 per sold unit.
a)
p = q + 80
(
2p − q = 50
b)
pq = 100 + 2q
7. A company selling dryers has fixed costs of $5250, and variable costs of 100 + 0.1x
per unit.
a) Write the formula for the cost function C(x).
b) If the selling price for a dryer is $210, calculate the profit function P (x) and find
the break-even point(s).