• anonymous
Need serious help on this one. An initial population of 655 quail increases at an annual rate of 18%. Write an exponential function to model the quail population.
  • Stacey Warren - Expert
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  • chestercat
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  • ZeHanz
General formula for this is \[P(t)=b⋅g^t\]where P is the population at time t, b is the population at the beginning (t=0) and g is the growing factor. I'd say b = 655. Do you know how to get from 18% increase per year to the growing factor per year?
  • campbell_st
why not just use the compound interest formula A = P(1 + r/100)^t \[A = 665(1 + \frac{18}{100})^t\]
  • ZeHanz
Well that is just the same as realising that 18% increase means you now have 110%+18%=118%. So the amount is multiplied with 1.18, making the formula:\[P(t)=655 \cdot 1.18^t\] In the end, it's all the same...

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