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anonymous

  • one year ago

MEDAL/FAN There are 30 homes in Neighborhood A. Each year, the number of homes increases by 20%. Just down the road, Neighborhood B has 45 homes. Each year, 3 new homes are built in Neighborhood B. Part C: After approximately how many years is the number of homes in Neighborhood A and Neighborhood B the same? Justify your answer mathematically.

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  1. anonymous
    • one year ago
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    @Kainui @mathway

  2. DanJS
    • one year ago
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    Was part A and B to come up with the equations to model both those situations?

  3. anonymous
    • one year ago
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    Part A:Neighborhood A:y=30(1.2)^x Neighborhood B: y=40+3x Part B: I just substitute x for 5. Neighborhood A's work: y=30(1.2)^5 y=30*2.48832 y=74.6494, or around 75 houses. Neighborhood B's work: y=40+3*5 y=40+15 y=55, so 55 houses @DanJS my answers^

  4. DanJS
    • one year ago
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    ok...

  5. DanJS
    • one year ago
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    Part C wants you to figure the years X, when both are equal # houses

  6. DanJS
    • one year ago
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    30(1.2)^x = 40 + 3x

  7. anonymous
    • one year ago
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    I know but I dont know what number to start at

  8. DanJS
    • one year ago
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    Oh, you have 40 for neighborhood B, it is 45 30(1.2)^x = 45 + 3x

  9. DanJS
    • one year ago
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    So recalculate part B for that one

  10. anonymous
    • one year ago
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    you sure? Okay so final houses=60

  11. DanJS
    • one year ago
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    "Neighborhood B has 45 homes. Each year, 3 new homes are built ", less the prob is typed wrong

  12. anonymous
    • one year ago
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    its right; 45

  13. anonymous
    • one year ago
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    /?What number should I START with

  14. anonymous
    • one year ago
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    20% of 30 is 6 so you could just use process of elimination. 3*5=15 15+45=60 5*6=30 30+30=60 so after 5 years they will be the same

  15. anonymous
    • one year ago
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    30(1.2)^5 does not equal 60

  16. anonymous
    • one year ago
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    @david422

  17. anonymous
    • one year ago
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    where did you get 30(1.2)^5??

  18. anonymous
    • one year ago
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    y=30(1.2)^x

  19. anonymous
    • one year ago
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    The equation from part one

  20. anonymous
    • one year ago
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    @DanJS

  21. anonymous
    • one year ago
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    idk i just went off what your initial question was

  22. anonymous
    • one year ago
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    well the equations are: Neighborhood A:y=30(1.2)^x Neighborhood B: y=45+3x

  23. anonymous
    • one year ago
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    @DanJS

  24. anonymous
    • one year ago
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    @ali2x2

  25. anonymous
    • one year ago
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    @Kainui

  26. anonymous
    • one year ago
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    @Afrodiddle @zepdrix

  27. DanJS
    • one year ago
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    sorry back, here is the graph

  28. DanJS
    • one year ago
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    the intersection is the point you need

  29. anonymous
    • one year ago
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    okay so when x=3.32, the two points intersect

  30. anonymous
    • one year ago
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    3.321 i meant

  31. DanJS
    • one year ago
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    yes, when 3.32 years have passed , both have same number of houses at near 55

  32. anonymous
    • one year ago
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    okay, thanks!

  33. DanJS
    • one year ago
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    i just asked a question about that form of equation...

  34. DanJS
    • one year ago
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    welcome

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