anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
do you mean 1.03 to the power of x...like so\[P=24.455*(1.03)^{x}\]
anonymous
  • anonymous
\[\log(30000/24455)/\log(1.03)\]
anonymous
  • anonymous
yes

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anonymous
  • anonymous
do you see what i did there?
anonymous
  • anonymous
\[P=30000=24455(1.03)^{x}=> (30000/24455)=1.03x => (\log(30000/24455)/\log(1.03)=x)\]
anonymous
  • anonymous
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
anonymous
  • anonymous
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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