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anonymous

  • 5 years ago

In 2007 the population of the town of Cartersville was 24,455. The population growth can be represented by the formula P = 24,455(1.03)x, where x represents the number of years after 2007. When will the population of the town first exceed 30,000?

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  1. anonymous
    • 5 years ago
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    do you mean 1.03 to the power of x...like so\[P=24.455*(1.03)^{x}\]

  2. anonymous
    • 5 years ago
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    \[\log(30000/24455)/\log(1.03)\]

  3. anonymous
    • 5 years ago
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    yes

  4. anonymous
    • 5 years ago
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    do you see what i did there?

  5. anonymous
    • 5 years ago
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    \[P=30000=24455(1.03)^{x}=> (30000/24455)=1.03x => (\log(30000/24455)/\log(1.03)=x)\]

  6. anonymous
    • 5 years ago
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    oh it cut off the rest, but then then take the log of both sides and divide by log(1.03) to solve for x

  7. anonymous
    • 5 years ago
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    so the answer then becomes 6.91 years when it equals 30000. The population will exceed 30 000 if x>6.91 [you can click become a fan now]

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