1. A company charting its profits notices that the relationship between the number of units bought, x, and the revenue, P, is linear. If 190 units bought leads to $380 revenue and 240 units bought leads to $2980 revenue, write the revenue perform for this company.
P = _________
Discover the marginal revenue.
$____________
2. A company distributes faculty brand sweatshirts and sells them for $45 every. The overall price perform is linear, and the whole price for 90 sweatshirts is $3951, whereas the whole price for 260 sweatshirts is $5991.
(a) Write the equation for the income perform R(x).
R(x) = ___________
(b) Write the equation for the whole price perform C(x).
C(x) = ____________
(c) Discover the break-even amount.
x = __________ sweatshirts
three. Suppose a sure residence enchancment outlet is aware of that the month-to-month demand for framing studs is 2,500 when the worth is $four.25 every however that the demand is three,700 when the worth is $three.89 every. Assuming that the demand perform is linear, write its equation. Use p for worth (in dollars) and q for amount.
________________
four. It has been estimated that a sure stream can help 88,000 fish whether it is pollution-free. It has additional been estimated that for every ton of pollution in the stream, 1500 fewer fish could be supported. Assuming that the relationship is linear, write the equation that offers the inhabitants of fish p in phrases of the tons of pollution x.
________________
5. An electrical utility company determines the month-to-month invoice for a residential buyer by including an vitality cost of 7.34 cents per kilowatt-hour to its base cost of $18.39 per thirty days. Write an equation for the month-to-month cost y in phrases of x, the number of kilowatt-hours used. (Let y be measured in dollars.)
________________
6. Suppose that from 2020 to 2060, the number of females in the U.S. beneath the age of 18, in hundreds of thousands, could be modeled by
N = zero.140x + 38.four
the place x is the number of years after 2020.
(a) Viewing N as a perform of x, what’s the slope m of the graph of this perform?
m = _________
(b) What does the mannequin predict the inhabitants of females beneath 18 (in hundreds of thousands) can be in 2040?
__________million.
7.
eight. A live performance promoter must make $79,600 from the sale of 1740 tickets. The promoter fees $40 for some tickets and $60 for the others. Let x signify the number of $40 tickets and y signify the number of $60 tickets.
(a) Write an equation that states that the sum of the tickets bought is 1740.
______________
(b) Write an expression for a way a lot cash is acquired from the sale of $40 tickets?
______________
(c) Write an expression for a way a lot cash is acquired from the sale of $60 tickets?
_________________
(d) Write an equation that states that the whole quantity acquired from the sale is $79,600
___________________
(e) Clear up the equations concurrently to seek out what number of tickets of every sort should be bought to yield the $79,600.
x= ____________
y= ____________
9. If the demand for a pair of footwear is given by 2p + 5q = 200 and the provide perform for it’s p − 2q = 10, evaluate the amount demanded and the amount provided when the worth is $90.
amount demanded ___________ pairs of footwear
amount provided ____________ pairs of footwear
10. Discover the market equilibrium level for the following demand and provide features.
Demand: p = −4q + 312 Provide: p= 6q + 1
(q, p) = ( __________ )
11. Discover the equilibrium level for the following provide and demand features.
Demand: p = −4q + 220 Provide: p= 16q + 20
(q, p) = ( __________ )
12. Retailers will purchase 45 Wi-Fi routers from a wholesaler if the worth is $10 every however solely 20 if the worth is $85. The wholesaler will provide 56 routers at $46 every and 70 at $50 every. Assuming that the provide and demand features are linear, discover the market equilibrium level.
(q, p) = ( __________ )
13.
(b) How lengthy is it till the constructing is totally depreciated (its worth is zero)?
__________months
(c) The purpose (70, 225,000) lies on the graph. Clarify what this implies.
The purpose (70, 225,000) means that after ________ months the worth of the constructing can be $ _____________ .
