A vendor at a carnival sells cotton candy and caramel apples for $ 2.00 each. The vendor is charged $ 100 to set up his booth. Furthermore, the vendor's average cost for each product he produces is approximately $ 0.75 . a. Write a linear cost function representing the cost C x in $ to the vendor to produce x products. b. Write a linear revenue function representing the revenue R x in $ for selling x products. c. Determine the number of products to be produced and sold for the vendor to break even. d. If 60 products are sold, will the vendor make money or lose money?
A vendor at a carnival sells cotton candy and caramel apples for $ 2.00 each. The vendor is charged $ 100 to set up his booth. Furthermore, the vendor's average cost for each product he produces is approximately $ 0.75 . a. Write a linear cost function representing the cost C x in $ to the vendor to produce x products. b. Write a linear revenue function representing the revenue R x in $ for selling x products. c. Determine the number of products to be produced and sold for the vendor to break even. d. If 60 products are sold, will the vendor make money or lose money?
A vendor at a carnival sells cotton candy and caramel apples for
$
2.00
each. The vendor is charged
$
100
to set up his booth. Furthermore, the vendor's average cost for each product he produces is approximately
$
0.75
.
a. Write a linear cost function representing the cost
C
x
in $
to the vendor to produce
x
products.
b. Write a linear revenue function representing the revenue
R
x
in $
for selling
x
products.
c. Determine the number of products to be produced and sold for the vendor to break even.
d. If
60
products are sold, will the vendor make money or lose money?
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
College Algebra with Modeling & Visualization (5th Edition)
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