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anonymous

  • 5 years ago

A colony of insects grows exponentially from 100 to 146 in one week. How many DAYS does it take for the population to reach 1300? A) 39 days B) 43 days C) 47 days D) 51 days E) 55 days

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  1. amistre64
    • 5 years ago
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    100 + x^7 = 146

  2. amistre64
    • 5 years ago
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    x^7 = 46 x = 46^(1/7) right?

  3. anonymous
    • 5 years ago
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    Correct.. can I ask how you got the first equation?

  4. amistre64
    • 5 years ago
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    the first equationis the inital value then simply add the exponential growth to it

  5. amistre64
    • 5 years ago
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    we know that it starts at 100 so.. 100 +..... add the exponential growth in at 7days 100 + x^7.....now that should equal 146 my exponential part my be in error, but its basically that

  6. amistre64
    • 5 years ago
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    the exponent i believe is measured in time units... to we need to calibrate it for the base unit....is my reasoning for picking x^7

  7. amistre64
    • 5 years ago
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    soo.... 100 + 46^(1/7)^d = 1300 ; where d is in days 46^(d/7) = 1200 d/7 log(46) = log(1200) d/7 = log(1200)/log(46) d = 7(log1200)/log(46)

  8. amistre64
    • 5 years ago
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    d = 12.96 days if we do it that route...gotta adjust for my stupidity herelol...hold on

  9. amistre64
    • 5 years ago
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    ack!!...thats it if i did it right; but apparently i messed up in the exponential department ;)

  10. amistre64
    • 5 years ago
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    x{n+1} = ax{n} + b .... recurrsion formulas, the bane of my existence

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