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12) (7 points) A-small towns population is expected to decrease 6% each year. There are currently 2750 people living in the

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Answer #1

Initial Population = 2750

r = 6% = 0.06

a) Population after t years is given by

    P(t) = Initial\, Population *(1 - r)^t

=> P(t) = 2750(1 - 0.06)^t

=> P(t) = 2750(0.94)^t

Therefore,

  P(t) = 2750(0.94)^t

b) In this case, P(t) = 600

    Therefore,

    600 = 2750(0.94)^t

   => (0.94)^t = 600 / 2750

   => ln ((0.94)^t) = ln (600 / 2750)

   => t ln (0.94) = ln (600 / 2750)

   => t = ln (600 / 2750) / ln (0.94)

   => t = 24.605

     Therefore,

    Answer: 24.605 years

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