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Math 120 – 03: Quiz #6: Thru Section 2.4
Fall 2013
Name:
1. Solve each of the following linear equations.
(a) 4x ! 7 = 30
(5 points each)
(b) 5 ( x !1) + 2 = 3 ( x + 8)
2. The number J, in thousands, of cans of frozen orange juice sold weekly is a function of the
price P, in dollars, of a can. In a certain grocery store, the formula is J = 11! 2.5P .
(a) Express using function notation the number of cans sold weekly if the price of a can
is $1.40, and then calculate that value. (4 points)
(b) At what price will 7250 cans be sold weekly at this store?
(6 points)
(c) Solve for P in terms of J and explain what that formula represents.
(6 points)
3. Solve each of the following by factoring or using the quadratic formula.
(a) x 2 ! 6x !16 = 0
(b) x 2 ! 30 = 7x
4. Solve each of the following using the crossing graphs method.
(a) 3.4e x = 87.687
(5 points each)
(5 points each)
(b) x 2 ! x 3 + 3 =
x5
20
5. A breeding group of foxes is introduced into a protected area, and the population growth
follows a logistic pattern modeled by the formula below where x is the number of years since
the group was introduced to the area.
N=
56.25
foxes
0.25 + 0.76 x
(a) How many foxes were introduced to this area?
(4 points)
(b) How long before the population grows to 150 foxes? Show your graph.
(6 points)
6. The temperature of a fresh cup of coffee, C, x minutes after it is poured is given by the
formula C = 125e!0.03x + 75 degrees Fahrenheit.
(a) What is the temperature of the coffee when it is first poured? Express your answer
using function notation. (4 points)
(b) The coffee is cool enough to drink once it has cooled to 150°F. When will the coffee
be cool enough to drink? Show the graph used to find this. (6 points)
(c) What is the temperature in the room? Hint: If the coffee is left to cool indefinitely, it
would cool to the room temperature. Support your answer. (6 points)