anonymous
  • anonymous
I need some help please. Write a function rule to describe each statement... the cost in dollars of printing dollar bills when it costs 3.8cents to print a dollar bill. the amount of money you earn mowing lawns at $15 per lawn. the profit you make selling flowers at $1.50 each when each flower costs you $.80
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
it costs 3.8 cents to print 1 dollar its costs 2 times 3.8 cents to print two dollars it costs 3 times 3.8 cents to print 3 dollars you can see a pattern here right?
anonymous
  • anonymous
yeah,but how do i write them as function rules?
anonymous
  • anonymous
we use variables! there should be two of them; one will represent the number of dollars, lets call that x and the other will represent the cost to print them, lets call that y

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anonymous
  • anonymous
my teacher told me to write the functions as f(x)=...
anonymous
  • anonymous
ok lets use f(x) instead of y so the cost to print, f(x), should equal the number of dollars, x, times 3.8 cents
anonymous
  • anonymous
so f(x)=3.8x
anonymous
  • anonymous
yes
anonymous
  • anonymous
ok so then for the second one would it be... f(x)=$15x
anonymous
  • anonymous
yep
anonymous
  • anonymous
but actually I made a mistake on the first one
anonymous
  • anonymous
I d dont understand how to write the third one though.
anonymous
  • anonymous
the function for the first part should give us the cost in dollars, with f(x) = 3.8x we'll end up with the number of cents
anonymous
  • anonymous
so you just convert 3.8 cents into dollars which should be .038
anonymous
  • anonymous
the profit you make selling flowers at $1.50 each when each flower costs you $.80
anonymous
  • anonymous
what is the profit if I sell one flower?
anonymous
  • anonymous
70 cents
anonymous
  • anonymous
right.. and if i sell two flowers?
anonymous
  • anonymous
a dollar and 40 cents
anonymous
  • anonymous
which is the same as 2 times 70 cents right? if I sell 3 flowers the profit would be 3 times 70 cents and if I sell x flowers the profit will be x times 70 cents
anonymous
  • anonymous
ok so... would the function be f(x)=.70x?
anonymous
  • anonymous
yes! good job
anonymous
  • anonymous
Thanks. Now i have another question i have this equation... f(x)=$0.59x where x+number of pounds. if i had $10 to buy that turkey how big a turkey could i buy?
anonymous
  • anonymous
you have f(x) = $0.59x which in words is, the cost of a turkey, f(x), is the number of pounds, x, times 59 cents
anonymous
  • anonymous
so the cost of a turkey is a function of the number of pounds that it weighs, does that make sense so far?
anonymous
  • anonymous
yeah. i was wondering where you d plug in the $10.
anonymous
  • anonymous
the ten dollars goes where dollars is represented in the equation
anonymous
  • anonymous
x is pounds f(x) is dollars so the equation, when we put in 10 dollars, becomes $10 = $0.59x
anonymous
  • anonymous
and by solving for x you will have found out how big a turkey you could by with 10 dollars
anonymous
  • anonymous
does that make sense?
anonymous
  • anonymous
16.95lb. is what i got. Yeah it does make sense.
anonymous
  • anonymous
|dw:1350441039671:dw|
anonymous
  • anonymous
|dw:1350441111447:dw|
anonymous
  • anonymous
i dont see the rule for either of these. It says to write a function rule. By the way.. they are two seperate questions.
anonymous
  • anonymous
ok lets start with the top one we need to find a way to relate x and y in other words we need to be able to describe how much y changes when x changes we can do this with a function y = x times (some number)
anonymous
  • anonymous
i know that,but idk what number it should be.,
anonymous
  • anonymous
we can find out what number it is by calculating the slope between the points that are given
anonymous
  • anonymous
with m = (y2-y1)/(x2-x1)
anonymous
  • anonymous
ok. so what should i get?
anonymous
  • anonymous
lets use the points: (0,1) and (1,3) m = (3-1)/(1-0) = 2
anonymous
  • anonymous
i understand it for the second table the answer would be f(x)=-4.5x. But i still dont see a pattern in the first one.
anonymous
  • anonymous
maybe graphing the points and seeing them line up would help
anonymous
  • anonymous
the y's are going up by two except for the last one.
anonymous
  • anonymous
because its a negative x in the last one, if it were positive 3 then y would be 7
anonymous
  • anonymous
|dw:1350442466454:dw|
anonymous
  • anonymous
thats the pattern if we follow the negative x points
anonymous
  • anonymous
the reason it isnt as easy to see as the second problem is because this function will have the form y = mx + b
anonymous
  • anonymous
whereas the second one was just y = mx
anonymous
  • anonymous
ok so whats the function rule.
anonymous
  • anonymous
well we're using y = mx + b as the template for our function, we found m to be 2, now we need to find b
anonymous
  • anonymous
so we have y = 2x + b since we're given points we can substitute one in for the values of x and y, and then solve for b so if we use (0,1) as our point we get 1 = 2(0) + b so b = -1
anonymous
  • anonymous
and keep in mind that we could have used any of the points that were given for example if we used (2,5) we get 5 = 2(2) +b and again b = -1
anonymous
  • anonymous
so now that we know b, we can finally write the function as y = 2x -1
anonymous
  • anonymous
thank you.
anonymous
  • anonymous
np :)

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