A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio C x to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue R x for holding x private lessons for the month. c. Write a linear profit function representing the profit P x for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
A dance studio has fixed monthly costs of $1500 that include rent, utilities, insurance, and advertising. The studio charges $60 for each private lesson, but has a variable cost for each lesson of $35 to pay the instructor. a. Write a linear cost function representing the cost to the studio C x to hold x private lessons for a given month. b. Write a linear revenue function representing the revenue R x for holding x private lessons for the month. c. Write a linear profit function representing the profit P x for holding x private lessons for the month. d. Determine the number of private lessons that must be held for the studio to make a profit. e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
A dance studio has fixed monthly costs of
$1500
that include rent, utilities, insurance, and advertising. The studio charges
$60
for each private lesson, but has a variable cost for each lesson of
$35
to pay the instructor.
a. Write a linear cost function representing the cost to the studio
C
x
to hold
x
private lessons for a given month.
b. Write a linear revenue function representing the revenue
R
x
for holding
x
private lessons for the month.
c. Write a linear profit function representing the profit
P
x
for holding
x
private lessons for the month.
d. Determine the number of private lessons that must be held for the studio to make a profit.
e. If 82 private lessons are held during a given month, how much money will the studio make or lose?
2. Suppose the population of Wakanda t years after 2000 is given by the equation
f(t) = 45000(1.006). If this trend continues, in what year will the population reach 50,000
people? Show all your work, round your answer to two decimal places, and include units. (4
points)
3. Solve the equation, give the answer exactly (no calculator approximations), and show all your
work. (4 points)
log5 2x = 3
Let I =
f(x) dx, where f is the function whose graph is shown.
4
2
y
f
X
1
2
3
4
(a) Use the graph to find L2, R2 and M2.
R₂
M2
=
=
=
(b) Are these underestimates or overestimates of I?
O 42 is an underestimate.
O 42 is an overestimate.
◇ R2 is an underestimate.
OR2 is an overestimate.
OM2 is an underestimate.
○ M2 is an overestimate.
(c) Use the graph to find T2.
T₂ =
College Algebra with Modeling & Visualization (5th Edition)
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