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100
While driving back to college after spring break, a student realizes that his distance from home, D, in miles, is given by D = 55t + 30, where t is the time in hours since the student made the realization. Give the initial value and the slope and what they mean.
Initial value = 30 miles from home slope = 55 miles per hour
100
The number of people, P, remaining in a lecture hall m minutes after the start of a very boring lecture is given by P = 300 - 19m/3. Give the initial value and the slope and what they mean.
initial value = 300 people slope = -19/3 (every three minutes, 19 people leave)
100
Express as a linear function: The population of a town after y years if the initial population is 23,400 and decreases by 200 people per year.
P = 23,400 - 200y
100
Express as a linear function. A company's cumulative operating costs after m months if it needs $7600 for equipment, furniture, etc. and if the rent is $3400 for each month.
C = 7600 + 3400m
100
Express as a linear function: A driver's distance from home after h hours if she starts 200 miles from home and drives 50 miles per hour away from home.
D = 200 + 50h
200
Express as a linear function: P = h(t) gives the size of a population at time t in years, that begins with 12,000 members and grows by 225 members each year.
P = 12,000 + 225t
200
The number of viewers for a new TV show is 8 million for the first episode. It drops to half this level by the fifth episode. Assuming viewership drops at a constant rate, find a formula for p(n), the number of viewers (in millions) for the nth episode.
p(n) = 8 - 0.8n
200
Identify the constants b and m: g(t) = 77t - 46
b = -46 m = 77
200
Identify the constants b and m: p(t) = 0.003
p(t) = 0t + 0.003 b = 0.003 m = 0
200
Evaluate the expression given that w(x) = 9 + 4x. Simplify. w(x-4)
w(x-4) = 9 + 4(x-4) = 9 + 4x - 16 = 4x - 7.
300
Is the expression linear? 3x - 2x2
no
300
Does 3x + 5 = 7 have a positive solution, a negative solution, a zero solution, or no solution?
Positive
300
Solve F = (9/5)C + 32 for C.
C = (5/9)(F-32)
300
Write the equation y - 8 = 3(x - 5) in the form y = b + mx.
y = 3x - 7
300
Put the equation 3x = 2y - 1 in standard form.
3x - 2y = -1
400
Write an equation in slope-intercept form that passes through (4, 6) with slope m = 2.
y = 2x - 2
400
Write an equation in slope-intercept form that contains (6, 8) and (8, 12).
y = -4 + 2x
400
Write an equation in slope-intercept form for the line that contains (4, 7) and is parallel to y = (1/2)x - 3.
y = 5 + (1/2)x
400
Find the formula for the linear function of the graph that intercepts the x-axis at x = 30 and the y-axis at y = -80.
y = (8/3)x - 80
400
Find the formula for the linear function: The total cost C of an international call lasting n minutes if there is a connection fee of $2.95 plus an additional charge of $0.35/minute
C = 2.95 + .35m
500
Find a formula for the linear function: The graph of f(x) passes through (-1, 4) and (2, -11).
f(x) = -5x - 1
500
Solve the system of equations: 2n + 7m = 1; 3n + 10m = 3
n = 11, m = -3
500
Solve the system of equations: 2v + 3w = 11; 2w - 3v = 29
w = 7, v = -5
500
Water is added to a barrel at a constant rate for 25 minutes, after which it is full. The quantity of water in the barrel after t minutes is 100 + 4t gallons. What do the 100 and 4 mean in practical terms? How much water can the barrel hold?
100 is how much water started in the barrel and it is being added at a rate of 4 gallons/minute. It can hold 200 gallons.
500
A party facility charges $500 for a banquet room and $20 per person. In addition there is a 20% surcharge on the entire fee. Why would you expect the total cost of the party to be given by a linear function of the number of people, P? Give the function
C = 500 + 20C, each person is charged the same amount of money.