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rebelchick777

  • 3 years ago

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

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  1. tjones89
    • 3 years ago
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    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?

  2. rebelchick777
    • 3 years ago
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    yeah,but how do i write them as function rules?

  3. tjones89
    • 3 years ago
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    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

  4. rebelchick777
    • 3 years ago
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    my teacher told me to write the functions as f(x)=...

  5. tjones89
    • 3 years ago
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    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

  6. rebelchick777
    • 3 years ago
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    so f(x)=3.8x

  7. tjones89
    • 3 years ago
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    yes

  8. rebelchick777
    • 3 years ago
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    ok so then for the second one would it be... f(x)=$15x

  9. tjones89
    • 3 years ago
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    yep

  10. tjones89
    • 3 years ago
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    but actually I made a mistake on the first one

  11. rebelchick777
    • 3 years ago
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    I d dont understand how to write the third one though.

  12. tjones89
    • 3 years ago
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    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

  13. tjones89
    • 3 years ago
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    so you just convert 3.8 cents into dollars which should be .038

  14. rebelchick777
    • 3 years ago
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    the profit you make selling flowers at $1.50 each when each flower costs you $.80

  15. tjones89
    • 3 years ago
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    what is the profit if I sell one flower?

  16. rebelchick777
    • 3 years ago
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    70 cents

  17. tjones89
    • 3 years ago
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    right.. and if i sell two flowers?

  18. rebelchick777
    • 3 years ago
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    a dollar and 40 cents

  19. tjones89
    • 3 years ago
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    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

  20. rebelchick777
    • 3 years ago
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    ok so... would the function be f(x)=.70x?

  21. tjones89
    • 3 years ago
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    yes! good job

  22. rebelchick777
    • 3 years ago
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    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?

  23. tjones89
    • 3 years ago
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    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

  24. tjones89
    • 3 years ago
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    so the cost of a turkey is a function of the number of pounds that it weighs, does that make sense so far?

  25. rebelchick777
    • 3 years ago
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    yeah. i was wondering where you d plug in the $10.

  26. tjones89
    • 3 years ago
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    the ten dollars goes where dollars is represented in the equation

  27. tjones89
    • 3 years ago
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    x is pounds f(x) is dollars so the equation, when we put in 10 dollars, becomes $10 = $0.59x

  28. tjones89
    • 3 years ago
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    and by solving for x you will have found out how big a turkey you could by with 10 dollars

  29. tjones89
    • 3 years ago
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    does that make sense?

  30. rebelchick777
    • 3 years ago
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    16.95lb. is what i got. Yeah it does make sense.

  31. rebelchick777
    • 3 years ago
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    |dw:1350441039671:dw|

  32. rebelchick777
    • 3 years ago
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    |dw:1350441111447:dw|

  33. rebelchick777
    • 3 years ago
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    i dont see the rule for either of these. It says to write a function rule. By the way.. they are two seperate questions.

  34. tjones89
    • 3 years ago
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    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)

  35. rebelchick777
    • 3 years ago
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    i know that,but idk what number it should be.,

  36. tjones89
    • 3 years ago
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    we can find out what number it is by calculating the slope between the points that are given

  37. tjones89
    • 3 years ago
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    with m = (y2-y1)/(x2-x1)

  38. rebelchick777
    • 3 years ago
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    ok. so what should i get?

  39. tjones89
    • 3 years ago
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    lets use the points: (0,1) and (1,3) m = (3-1)/(1-0) = 2

  40. rebelchick777
    • 3 years ago
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    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.

  41. tjones89
    • 3 years ago
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    maybe graphing the points and seeing them line up would help

  42. rebelchick777
    • 3 years ago
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    the y's are going up by two except for the last one.

  43. tjones89
    • 3 years ago
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    because its a negative x in the last one, if it were positive 3 then y would be 7

  44. tjones89
    • 3 years ago
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    |dw:1350442466454:dw|

  45. tjones89
    • 3 years ago
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    thats the pattern if we follow the negative x points

  46. tjones89
    • 3 years ago
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    the reason it isnt as easy to see as the second problem is because this function will have the form y = mx + b

  47. tjones89
    • 3 years ago
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    whereas the second one was just y = mx

  48. rebelchick777
    • 3 years ago
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    ok so whats the function rule.

  49. tjones89
    • 3 years ago
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    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

  50. tjones89
    • 3 years ago
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    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

  51. tjones89
    • 3 years ago
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    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

  52. tjones89
    • 3 years ago
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    so now that we know b, we can finally write the function as y = 2x -1

  53. rebelchick777
    • 3 years ago
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    thank you.

  54. tjones89
    • 3 years ago
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    np :)

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