Let t =number of years of operation.
20) A formula for the total cost of heating by gas, in terms of t, would be
a) C(t) = 12, 000t + 700
b) C(t) = 12, 000 + 700t
c) C(t) = 30, 000t + 150
d) C(t) = 30, 000 + 150t
21) An estimate of the total cost after 20 years of operation, if solar heating
is used
would be
a) $30,020
b) $30,150
c) $33,000
d) $600,150
22) Look at the graphs of the two functions (on the same graph). The
number of years of operations (after installation) it takes for the total cost of
solar to become less expensive than the total cost of gas is
a) about 20 years
b) about 33 years
c) about 35 years
d) about 42 years
23−24
Values for the functions F (t), G(t), and H(t) are given below.
t F (t) G(t) H(t)
1 237
58
50.4
2 301
49
49.5
3 383
41
48.6
4 487
34
47.7
5 619
28
46.8
6 787
23
45.9
23) The function best represented by a line is
a) F (t)b) G(t)c) H(t)
24) Why did you choose the function you did in #23?
4
b) . . . will give different answers, depending on the x values.
c) . . . will give answers that are within three decimal places of one
another.
d) You can’t tell without more information.
14) Horizontal lines have . . .
a) . . . no slope.
b) . . . a slope equal to the y-intercept.
c) . . . a slope of zero.
d) . . . an undefined slope.
15) If
a) .
b) .
c) .
d) .
y = f(x) is a decreasing function, then . . .
. . y decreases as x decreases.
. . y increases as x decreases.
. . y decreases as x increases.
. . y increases as x increases.
16) For a decreasing exponential function, P (x) = Po ax ,
a) a < 0
b) a > 0
c) 0 < x < 1
d) 0 < a < 1
17) The function below which does not have a change in concavity is
a) exponential
b) cubic
c) logistic
d) surge
18) Given the cost function C(x) = 0.05x2 + 110, the fixed costs when
100
items are produced are
a) 110
b) 0.05
c) 5
d) 50
19) The function which will eventually dominate y = 1, 000, 000 x3 as
x → ∞ is
a) y = 1, 000, 000, 000, 000 x2
b) y = (x + 1)3
c) y = 0.004 x4
d) y = 108 x2 + 104 x
20−22 The following shows the typical cost for two different kinds of heating
systems for a three-bedroom housing unit.
Type of System
Gas
Solar
OperationCostP erY ear
(indollars)
InstallationCost
(indollars)
12,000
30,000
700
150
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c) 1.38 years
d) 11.90 years
7) When observing the value of y in the function y = −x5 , as x → −∞, then
y approaches
a) 0
b) ∞
c) −∞
d) x
8) The graph of y = 12 sin 2x has what amplitude and period?
a) amplitude 2 and period 12 π
b) amplitude 12 and period 2π
c) amplitude 2 and period π
d) amplitude 12 and period π
e) none of these
9-10 If the drug concentration curve for a certain drug is C = 10te−0.4t ,
where t is in hours,
9) How many hours will it take for the concentration to peak?
a) 5/2
b) 2/5
c) 4
d) 1/4
10) What is the concentration at the time that it peaks?
a) 9.197
b) 3.409
c) 8.076
d) 2.262
500
11-12 Given the logistic function F (t) = 1+49e
−0.5t , where t is in years,
11) What is the limiting value?
a) 500
b) 49
c) 50
d) 0.5
12) How long will it take until F (t) = 250 ?
a) 5 years
b) 7.78 years
c) 24.54 years
d) 250 years
13) Using any two points on a line to calculate the slope . . .
a) . . . will give the same answer.
2
MATH 115
Test 1
1) Given the following demand and supply curves, D(q) = −5q + 880 S(q) =
3q + 400 where q is the quantity and the price is in dollars. The equililbrium
price and quantity are
a) $60 each for 580 items
b) $580 each for 60 items
c) $400 each for 880 items
d) $880 each for 580 items
2) The line 2y + 5x − 8 = 0 has a slope of
a) −5/2
b) −2/5
c) 5/2
d) 2/5
3-4 A fraternity wants to sell Bradley University tee shirts. It costs $300 for
the “template” to print the tee shirts and then $5 for each shirt. The fraternity
will sell them for $15 per shirt.
3) An equation for the profit function, P (x), in terms of the number of shirts
x is
a) P (x) = 5x − 300
b) P (x) = 10x − 300
c) P (x) = 15x − 305
d) P (x) = 15x + 300
4) In order to break even the fraternity will have to sell how many shirts?
a) 60
b) 30
c) 20 13
d) 20
5-6 The population on a remote island is currently 500, and it is increasing
exponentially at the rate of 6% per year.
5) A formula for the population, P , as a function of time, t, in years is
a) P (t) = 500(0.06t)
b) P (t) = 500(0.06)t
c) P (t) = 5001.06t
d) P (t) = 500(1.06)t
6) The amount of time, in years, that it will take for the population to double
is
a) 33 13 years
b) 1000 years
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