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anonymous

  • 5 years ago

In 1977 the population of the United States was about 220 million and in 1987 the population was about 242. Assuming that the growth of population of the United States is an exponential function determine the year in which the population will reach 500 million. I need to find an equation for this but I haven't been able to figure it out

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  1. Yuki
    • 5 years ago
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    oh, remidia lol all of these problems are based on the fact\[N = N_0 (R)^{t/h}\]

  2. anonymous
    • 5 years ago
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    I know, but I dont know how to place things properly. I solved for 500 = 100(1.1)^ t/10 and got the wrong answer. Something in my equation is wrong (I think)

  3. anonymous
    • 5 years ago
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    (220)*R^10=242

  4. Yuki
    • 5 years ago
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    where N is the current amount N-0 is the initial amount R is the growth/decay rate (if R>1 growth, R<1 decay) t is time h is the rate life ( for example, it a bacteria increases it's population in 7 days where t is in weeks, h would be 7)

  5. Yuki
    • 5 years ago
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    the given facts are telling you that initially there are 220 and after "10 years" there are 242 the idea here is that in 10years, the population grows by 42million when initially there were 220 million since the population matters when you want to know how fast it grows, all we need now is the rate. h is a variable that converts the time unit, so since we will just be using "years" only, h =1 is fine. so the eqn we can make is \[242 = 200(R)^{10}\]

  6. Yuki
    • 5 years ago
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    so R is apprx \[1.21^{1/10}\]

  7. Yuki
    • 5 years ago
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    if you want to consider "population grows by 10th-rt(121)% per year" but a more natural way to think is "population grows by 121% per 10 years"

  8. Yuki
    • 5 years ago
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    so you use the function\[N = N_0(R)^{t/10}\]

  9. Yuki
    • 5 years ago
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    that way, you will figure out that R is just 1.21 and \[500 = 200(1.21)^{t/10}\]

  10. Yuki
    • 5 years ago
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    so you can solve for t

  11. Yuki
    • 5 years ago
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    I got about 48 years later, so about 2025 ?

  12. anonymous
    • 5 years ago
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    Thats what I got, but the choices are A) 2054 B) 2057 C) 2060 D) 2063 E) 2066 I think the 200 might be wrong

  13. Yuki
    • 5 years ago
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    ah, it was 220, wasn't it. let me calculate it again

  14. Yuki
    • 5 years ago
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    I got 2063 since it takes 86 years to grow that much

  15. anonymous
    • 5 years ago
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    How did you find the 86? Ahhhh im so confused.

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