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1. George has opened a new store and he is monitoring its success closely.

He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and  r(x) is measured in hundreds of dollars. 

He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and  c(x) is measured in hundreds of dollars.

 

What does (r−c)(3) mean about George's new store?

 

The new store will sell 3400 items in its third month in business.

The new store will sell 2400 items in its third month in business.

The new store will have a profit of $2400 after its third month in business.

The new store will have a profit of $3400 after its third month in business.

 

2. A horse-drawn carriage tour company has found that the number of people that take their tour depends on the price charged per customer. The more the company charges for a tour, the fewer people decide to take the tour.

The function c(x)=50+5x represents price charged per customer where x is the number of $5 increases they charge over a rate of $50 per person. 

The function  p(x)=100−2x represents the number of customers expected for the day, where x is the number of $5 increases they charge over a rate of $50 per person.

 

What does (p⋅c)(2) mean about the horse-drawn carriage tour company?

 

The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $40.

The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $40.

The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $60.

The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60

jbouyer  Feb 12, 2018
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2+0 Answers

 #1
avatar+531 
+1

x in months, r(x) & c(x) in $100 
r(x)=x²+6x+10 
c(x)=x²-4x+5 

(r-c)(x) = r(x)-c(x) = (10x+5) (×100) 
(r−c)(4) = (10(4)+5)(100) = 4500 
profit of $4500 

f(x)=4x²-5 
g(x)=x+3 
(f•g)(x) = f(x)•g(x) = (4x²-5)(x+3) 
= 4x³+12x²-5x-15 

f(x)=3x²+10x-8 = (3x-2)(x+4) 
g(x)=3x²-2x = x(3x-2) 
(f/g)(x) = f(x)/g(x) = [(3x-2)(x+4)]/[x(3x-2)] 
= (x+4)/x, x≠0,2/3

lynx7  Feb 12, 2018
 #2
avatar+85620 
+1

1.  (r - c) (3)  =   r(3)  - c(3)  =

 

r(3)  =  (3)^2+5(3)+14   = 38

c(3) =  (3)^2−3(3)+4  =    4

 

So   r(3)  - c(3)   =   38  - 4   =    34

 

The store makes a profit of $3400 in the third month of business

 

2.  (p * c) (2)   =  p(2) * c(2)  =

 

p(2)  = 100−2(2)   =  96

c(2)  = 50+5(2)  =  60

 

So

 

p(2) * c(2)   =   96 * 60  =  $5760  when the price per customer  = $60

 

 

cool cool cool

CPhill  Feb 12, 2018

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