anonymous
  • anonymous
Use an exponential model to solve the problem: The population of Knoxville is 500,000 and is increasing at the rate of 3.25% each year. Approximately when will the population reach 1 million?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@satellite73 please help
anonymous
  • anonymous
the population starts at 500000, lets just say at t=0 after the first year, t=1 the population is increased by 3.25% so the population would be 500000 + 500000 ( .0325) or 500000(1.0325) lets consider the next year t=2 the population increases another 3.25% from the last year so the population will now be 500000(1.0325)(1.0325) or \[500000(1.0325)^2\]
anonymous
  • anonymous
now considering the 3rd year, t=3 it would be 500000(1.0325)(1.0325)(1.0325) hopefully you see the pattern by now so if we were to write this as an equation for "t" years later it would look like \[P= 500000 (1.0325)^t\] where P is the total population at "t" years later

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anonymous
  • anonymous
in the case of your question, you want to determine the number of years it takes for the initial population of 500000 to reach 1 mil in which case, P= 1000000, and solve for t
anonymous
  • anonymous
any questions?
anonymous
  • anonymous
just one... for the equation 1000000=500000(1.0325)^t how do I get the exponent down?
anonymous
  • anonymous
natural log rules specifically power rule \[\ln ( x ^y) = y \ln (x)\]
anonymous
  • anonymous
got it thanks

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