Question

1)A linear cost function is

C(x) = 6x + 450. (Assume C is measured in dollars.)

(a) What are the slope and the C-intercept?

slope
C-intercept

(b) What is the marginal cost

MC ? MC=

What does the marginal cost mean?

Each additional unit produced costs this much (in dollars).

If production is increased by this many units, the cost decreases by $1.

Each additional unit produced reduces the cost by this much (in dollars).

If production is increased by this many units, the cost increases by $1.

(c) What are the fixed costs?
$  

(d) How are your answers to parts (a), (b), and (c) related?
slope = marginal cost, and C-intercept = fixed costs

slope = fixed costs, and C-intercept = marginal cost     

C-intercept/slope =marginal cost

slope/

C-intercept. =marginal cost

(e) What is the cost of producing one more item if 50 are currently being produced?
$  

What is the cost of producing one more item if 100 are currently being produced?
$

A linear revenue function is

R = 38.82x.

(a) What is the slope m
m =   

(b) What is the marginal revenue

MR?

MR =

What does the marginal revenue mean?

If the number of units sold is increased by this amount, the revenue increases by $1.

If the number of units sold is increased by this amount, the revenue decreases by $1.     

Each additional unit sold yields this many dollars in revenue.

Each additional unit sold decreases the revenue by this many dollars.

(c) What is the revenue received from selling one more item if 36 are currently being sold?
$  

What is the revenue received from selling one more item if 74 are being sold?
$

2)A concert promoter needs to make $77,800 from the sale of 1720 tickets. The promoter charges $40 for some tickets and $55 for the others. Let x represent the number of $40 tickets and y represent the number of $55 tickets.

(a) Write an equation that states that the sum of the tickets sold is 1720.

(b) Write a formula for how much money is received from the sale of $40 tickets?
$  

(c) Write a formula for how much money is received from the sale of $55 tickets?
$  

(d) Write an equation that states that the total amount received from the sale is $77,800.

(e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $77,800.

x	=
y	=

3) Carbon 14 (¹⁴C) dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of ¹⁴C absorbed by a tree that grew several centuries ago should be the same as the amount of ¹⁴C absorbed by a tree growing today. A piece of ancient charcoal contains only 23% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal given that the half-life of ¹⁴C is 5700 years? (Round your answer to the nearest whole number.)

4) If the population of a certain city was 100,000 in 1996 and 110,671 in 2006, and if the population grows exponentially, estimate the population of the city in 2021.
(use at least four decimal places for your rate, but round your FINAL ANSWER to the nearest whole number.)
people
yr

Answer 1

1. b) C(x)=6564450 = molta Slope =6 Slope cintercept = 40 marginal cost=slope =6 or a cloc) dx = Mariginal lost =d marginal lost: Each additional costs this much (in dollars) Te - 6 bort +4.50 =6 unit produced c)

Fixed cost = Intercelts uso slope = Marginal lost, Cintereelt=fixed lands Cost of producing Imore = marginal Cost ve G cost of protincing I more at loo=6 R=38.820L slope = 38.82 marginal revenue Ed -d 38.82 dx 2) 738.82

by Marginal revenre = 38.82 marginal revenire. Each additonal unit Yields this many dollars in revenue sold Marginal Revenue from telling I more revenue = $38.82 At Ih also $38.82 acty= 1720 ecco u sale of sale $ho tickets = you $55 tickets=55* of

oogtt -85S treh aty = 1720 Moolthoy=$68800 -(2) (1)-(2) Isac = gooo ac = Goo y=1720-60031220 3: Nlt) = MO (E) olet (1) 0.23= 10-515700 Nit) -1.46968 Inoos 00 -146968t -0.69315 5700 X-O. t = 57000(-1.4698) -0.69315 - 12085.68 yi Po portion 100,000 In 2006 t= 2006 - 1996 =10 110671 = 10ooooo bi 1.10671 = 60 In 1.10671 = lomb 0.101392 = lnb To 2001 – 2021-7996 = 25 100000x11101011?S=128850 1910.0 . 9 16106119